2D TRANSFORMATIONS (Contd.)
|
|
- Cody Briggs
- 8 years ago
- Views:
Transcription
1 AML7 CAD LECURE 5 D RANSFORMAIONS Con. Sequene of operons, Mr ulplon, onenon, onon of operons pes of rnsforon Affne Mp: A p φ h ps E 3 no self s lle n ffne Mp f leves renr onons nvrn. 3 If β j j,, j E hen, 3 φ β φ φ, φ E j j j Mos of he rnsforons h re use o poson or sle n oje n CAD re ffne ps. he ne ws gven L. Euler n sue ssell A. Mous Euln Mps: Rg o oons lke roon n rnslon where lenghs n ngles re unhnge re lle Euln ps. hs s spel se of ffne ps
2 rnsforon Groups n Seres Affne rnsforons re lssfe Fel Klen s follows Slr Groups: Rg oon n slng Eg: Congruen, slr Ser Groups:Roon, Refleon, rnslon. No rnslon n no refleon Crle group Eg: ger wheel. No rnslon n les one refleon Dherl group 3. rnslon long one reon. rnslon long ore hn one reon Hoogeneous oornes of veres A pon n hoogeneous oornes,, h, h, orrespons o he -D vere /h, /h n Cre oornes. Coneve h he Cre oornes es les on he plne of h. he nerseon of he plne n he lne onneng he orgn n,, h gves he orresponng Cre oornes. w,, h /h, /h, h h
3 For eple, oh he pons 6, 9, 3 n, 6, n he hoogeneous oornes orrespons o, 3 n he Cre oornes. Conversel, he pon, of he Cre orrespons o,,,,, or 6, 3, 3 of he hoogeneous sse h 6, 3, 3,,,, h h Roon Conser he followng fgure where poson veor p, whh kes n ngle φ o -s fer rnsforon o p, kes n ngle φ egrees. P, P [ ] [rosφ rφ] P [ ] [rosφ rφ ] [rosφos -φ rosφ φos ] Ug he efnon of rosφ n rφ, we n wre φ P [ ] [ os os ] or he rnsforon r s os [ X ][ ] [ ] os P, 3
4 Soe Coon Cses of Roon Roon of 9 ouner lokwse ou he orgn os [ ] os Roon of 8 ouner lokwse ou he orgn os os [ ] Roon of 7 ouner lokwse ou he orgn os os In ll he ove ses e[] [ ] Refleon- Spel se of Roon Refleon s spel se of roon of 8 ou lne n plne psg hrough he orgn. Eg ou -s Aou -s [ ] [ ] Aou he lnes n - respevel re: [ ] [ ]
5 Refleon- Properes If wo pure refleons ou lne psg hrough he orgn re pple suessvel he resul s pure roon. he eernn of pure refleon r s - [ ] Properes of rnsforon Mres De[]? In se of roon, refleon. Wh s he geoerl nerpreon of nverse of []? Show h - [I] os [ ] os os os os os [ ] hus for pure roon e[] he nverse of s s rnspose 5
6 6 Show h he followng rnsforon r gves pure roon ] [ ] e[ Eple Eple A A un squre s rnsfore rnsforon r. he resulng poson veors re: Deerne he rnsforon r use. Ans: ] [ 6 3 ] [ ; ] ][ [ ] [ X
7 7 Eple Show h he sher rnsforon n n reons ogeher s no he se s sher long followe sher long? Ans: Eple Prole Conser rngle whose veres re, n. Fn he onene rnsforon r n he rnsfore veres for roon of 9 ou he orgn followe refleon hrough he lne -. Coen on he sequene of rnsforons. } }[ [ } }[ }[ [ X X For seeng he effe of hngng he sequene of operons le us reverse he orer,.e, frs refleon n hen roon. } }[ [ } }[ }[ [ X X
8 8 Eple Prole: Soluon Conu onon of rnsforons n sequene rnsle he rgh-ngle vere o he orgn -, - Roe 5 o π / rn π / os π /.77, 5,,3.8,.8 -.,.,,,. ' ' ' w w ' ' ' os os " " " w w
9 9 os os os os os os ' ' ' os os " " " w w w w he opuon of [ ] fro [ ] [ ] s lle r ulplon. he generl for s: A sequene of rnsforons n e lupe n gle r v r ulplons h f g e h f g e h g f e Slng relve o fe pon. rnsle he pon-, -n o he orgn. Sle he oje S, S sle fors 3. rnsle he pon k, n, n [ ] [ ] [ ][ ] S [ ] n S S n Colun eors
10 Roon ou n rrr pon, n [ ] [ ][ ][ ] R [ ] os os n n Row eors Roon ou n rrr pon. rnsle he pon-, -n o he orgn. Roe he oje ou he orgn o 3. rnsle k,n E: Cener of n oje,3, roe ou he ener 9 o CC P [ h] [ ] [ ][ ][ ] R [ ] 7 7 OR P, n [ ] os os n n
11 Refleon O3 Refleon s spel se of roon SO3 when ngel of roon s 8 ou n s n he plne 8 [ ], os8 n Refleon ou n rrr lne. rnsle, - so h he lne psses hrough he orgn. Roe he lne ou he s - o 3. Refle oje ou he s. Roe k he lne o 5. rnsle k, [] [ ] [ ][ ][ R][ ] [ ] r r / / 5 5 / / 5 5 / / 5 5 / E: Refle rngle,,,6,,6 ou lne 3/5 /5 8/5 /5 3/5 6/5 6 6 / 5 5 /5 8/5 /5 /5 /5 6/5 n Alerne Meho?
12 M-pon rnsforon Conser srgh lne eween A, n B,. Le us r o rnsfor hs lne ug generl rnsforon r B M E B A F M A [ ] ] [ B A B A [ ] [ ] ' ' M-pon rnsforon Fro n we n onlue h reursvel onnung hs proess, we wll over ll pons on he lne AB n hene her ges on AB orresponng p. Bu generl proof of en pons rnsforon ull rnsfors he whole lne n e gven usgn he seon forul. An pon h ves he lne AB n he ro p:q n e gven s: Neeless o s h he se s pplle o AB. he spel se of pon rnsforon ours when p:q. B M E B A F M A q p q p
13 rnsforon of nerseng lnes When wo nerseng lnes re rnsfore ug generl rnsforon r he resulng lnes re lso nerseng Conser nerseon lnes he pon of nerseon: rnsfore pon of nerseon: [ X ] [ ] [ X ] E A A B F E F B ' ' [ ] rnsforon of nerseng lnes Oserve hese pons In he ls sle E. A pr of non-perpenulr lnes ge rnsfore o perpenulr lnes A B E B. B nverse - F pr of perpenulra lnes n ge rnsfore o non-perpenulr lnes 3. Suh resul n hve ssrous effe on he resulng geoer F 3
14 rnsforon of wo prllel lnes When wo prllel lnes re rnsfore ug generl rnsforon r he resulng lnes ren prllel Conser lnes prllel o eh oher eween he en pons A,,B, n CD. Sne he re prllel he slope s he se gven [ ][ ] X Inerseng lnes n rg o rnsforons When o perpenulr lnes rnsfor s perpenulr lnes? Conser he slro n veor prous of wo veors s follows Le us now rnsfor hese veors generl n fn o n ross prous gn We requre for gnue n ngle o ren unhnge os. k k v v os k k r r [ ][ ] [ ][ ] [ ] I OR ; ;
15 5 rnsforon of Un squre n re Oserve un squre eng sle n shere long n es sulneousl A B D C A D B C P n P ; ] e[ ] e[ s A p A p A, o,,, Are Slng eple A rngle wh veres,,, n -, s rnsfore Are eres fer rnsforon re rnsfore re, sq.uns A 3 [ ] [X '] sq.uns 8 A A
16 Geoerl Inerpreon of Overll Slng [ h] [ ] [ s] s s s h< h h> ewng rnsforons I s rnsforon fro worl CS o Sreen CS. he ensons of he WCS e n n hosen sse of uns SI or FPS e he ler s esure n pels.. rnsle he MCS se pon o orgn. Appl he slng neessr o f no he sreen ls n,n n 3. Move he se pon k o s orgnl poson [ ] [ ][ S][ ] [] n n u un n v vn n un vn 6
17 rnslon Wh re nvrn? Lenghs Angles Whh rnsforon group? Congruen e[] rnslon Dlon Wh re nvrn? Ro of Lenghs Angles Whh rnsforon group? slr e[] 7
18 rnslon Roon Wh re he nvrns? Lenghs Angles Whh rnsforon group? Congruen e[] Refleon Wh re he nvrns? Lenghs Angles Whh rnsforon group? Congruen e[] - 8
19 RefleonrnslonGle Wh re he nvrns? Lenghs Angles Whh rnsforon group? Congruen e[] - Gle R R Sher rnsforon Wh re nvrn? prllels - 5 Whh rnsforon group? ffne - 6 9
20 Projeve rnsforon Wh re nvrn? Inene Cross ros of lenghs Orer of urves Isoeres of Squre How n soeres? en Roonl Refleon Cle le of soeres of squre H D I H D D D h D D D H D D D H H H D D h v D D D H D D D H D D D D H 7 9 8
21 rnsforons Possle n fferen Geoeres rnsforon / Geoeres Euln Slr Affne Projeve Roon rnslon Unfor Slng Non-unfor Slng Sher Cenrl Projeon Invrn Qunes n fferen Geoeres rnsforon / Geoeres Euln Slr Affne Projeve Lenghs Angles Ros of Lenghs Prllels Inene Cross-ros of Lenghs
WHAT HAPPENS WHEN YOU MIX COMPLEX NUMBERS WITH PRIME NUMBERS?
WHAT HAPPES WHE YOU MIX COMPLEX UMBERS WITH PRIME UMBERS? There s n ol syng, you n t pples n ornges. Mthemtns hte n t; they love to throw pples n ornges nto foo proessor n see wht hppens. Sometmes they
More informationVector Algebra. Lecture programme. Engineering Maths 1.2
Leue pogmme Engneeng Mh. Veo lge Conen of leue. Genel noduon. Sl nd veo. Cen omponen. Deon one. Geome epeenon. Modulu of veo. Un veo. Pllel veo.. ddon of veo: pllelogm ule; ngle lw; polgon lw; veo lw fo
More informationSpline. Computer Graphics. B-splines. B-Splines (for basis splines) Generating a curve. Basis Functions. Lecture 14 Curves and Surfaces II
Lecure 4 Curves and Surfaces II Splne A long flexble srps of meal used by drafspersons o lay ou he surfaces of arplanes, cars and shps Ducks weghs aached o he splnes were used o pull he splne n dfferen
More informationLesson 2.1 Inductive Reasoning
Lesson.1 Inutive Resoning Nme Perio Dte For Eerises 1 7, use inutive resoning to fin the net two terms in eh sequene. 1. 4, 8, 1, 16,,. 400, 00, 100, 0,,,. 1 8, 7, 1, 4,, 4.,,, 1, 1, 0,,. 60, 180, 10,
More informationVectors Summary. Projection vector AC = ( Shortest distance from B to line A C D [OR = where m1. and m
. Slr prout (ot prout): = osθ Vetors Summry Lws of ot prout: (i) = (ii) ( ) = = (iii) = (ngle etween two ientil vetors is egrees) (iv) = n re perpeniulr Applitions: (i) Projetion vetor: B Length of projetion
More informationPhys222 W12 Quiz 2: Chapters 23, 24. Name: = 80 nc, and q = 30 nc in the figure, what is the magnitude of the total electric force on q?
Nme: 1. A pricle (m = 5 g, = 5. µc) is relesed from res when i is 5 cm from second pricle (Q = µc). Deermine he mgniude of he iniil ccelerion of he 5-g pricle.. 54 m/s b. 9 m/s c. 7 m/s d. 65 m/s e. 36
More informationLecture 40 Induction. Review Inductors Self-induction RL circuits Energy stored in a Magnetic Field
ecure 4 nducon evew nducors Self-nducon crcus nergy sored n a Magnec Feld 1 evew nducon end nergy Transfers mf Bv Mechancal energy ransform n elecrc and hen n hermal energy P Fv B v evew eformulaon of
More informationRevision: June 12, 2010 215 E Main Suite D Pullman, WA 99163 (509) 334 6306 Voice and Fax
.3: Inucors Reson: June, 5 E Man Sue D Pullman, WA 9963 59 334 636 Voce an Fax Oerew We connue our suy of energy sorage elemens wh a scusson of nucors. Inucors, lke ressors an capacors, are passe wo-ermnal
More informationHalley s Comet Project. Calculus III
Hlle s Come Projec Clculus III Come Hlle from Moun Wlson, 1986 "The dvers of he phenomen of nure s so gre, nd he resures hdden n he hevens so rch, precsel n order h he humn mnd shll never be lcng n fresh
More informationVectors. The magnitude of a vector is its length, which can be determined by Pythagoras Theorem. The magnitude of a is written as a.
Vectors mesurement which onl descries the mgnitude (i.e. size) of the oject is clled sclr quntit, e.g. Glsgow is 11 miles from irdrie. vector is quntit with mgnitude nd direction, e.g. Glsgow is 11 miles
More informationModule 5. Three-phase AC Circuits. Version 2 EE IIT, Kharagpur
Module 5 Three-hse A iruits Version EE IIT, Khrgur esson 8 Three-hse Blned Suly Version EE IIT, Khrgur In the module, ontining six lessons (-7), the study of iruits, onsisting of the liner elements resistne,
More informationA Novel Algorithm for Four Phase (Multi-phase) Source Side Load Balancing and Power Factor Correction
nterntonl Journl of Reent Trens n Engneerng, Vol, No. 3, My 009 A Novel Algorth for Four hse (Mult-phse Soure Se Lo Blnng n ower Ftor Correton Frst A. Zkr Husn, Seon B. R. K. Sngh n Thr C. S. N. Twr 3
More informationOrthopoles and the Pappus Theorem
Forum Geometriorum Volume 4 (2004) 53 59. FORUM GEOM ISSN 1534-1178 Orthopoles n the Pppus Theorem tul Dixit n Drij Grinerg strt. If the verties of tringle re projete onto given line, the perpeniulrs from
More informationCampus Sustainability Assessment and Related Literature
Campus Sustainability Assessment and Related Literature An Annotated Bibliography and Resource Guide Andrew Nixon February 2002 Campus Sustainability Assessment Review Project Telephone: (616) 387-5626
More informationA Network Traffic Flow Model for Motorway and Urban Highways
A Newor Tr Flow Moel or Moorwy n Urn Hghwys Cho Yng Rs Remenye-Preso John Anrews * Nonghm Trnsporon Engneerng Cenre Unversy o Nonghm NG7 RD Nonghm UK Asr The reserh repore n hs pper evelops newor level
More informationLOAD BALANCING AND POWER FACTOR CORRECTION FOR MULTIPHASE POWER SYSTEMS
nterntonl Journl of Ane Reserh n Engneerng n Tehnology (JARET) olue 7, ssue, Mrh-Aprl 6, pp. 9, Artle D: JARET_7 9 Alle onlne t http://www.ee.o/jaret/ssues.sp?jtype=jaret&type=7&type= Journl pt Ftor (6):
More informationMath 314, Homework Assignment 1. 1. Prove that two nonvertical lines are perpendicular if and only if the product of their slopes is 1.
Mth 4, Homework Assignment. Prove tht two nonverticl lines re perpendiculr if nd only if the product of their slopes is. Proof. Let l nd l e nonverticl lines in R of slopes m nd m, respectively. Suppose
More informationA Model for Time Series Analysis
Aled Mahemaal Senes, Vol. 6, 0, no. 5, 5735-5748 A Model for Tme Seres Analyss me A. H. Poo Sunway Unversy Busness Shool Sunway Unversy Bandar Sunway, Malaysa ahhn@sunway.edu.my Absra Consder a me seres
More informationMaximum area of polygon
Mimum re of polygon Suppose I give you n stiks. They might e of ifferent lengths, or the sme length, or some the sme s others, et. Now there re lots of polygons you n form with those stiks. Your jo is
More informationProjective geometry- 2D. Homogeneous coordinates x1, x2,
Projece geomer- D cknowledgemen Marc Pollefe: for allowng e ue of ecellen lde on opc p://www.c.unc.edu/~marc/mg/ Rcard arle and ndrew Zerman "Mulple Vew Geomer n Compuer Von" omogeneou coordnae omogeneou
More informationVectors 2. 1. Recap of vectors
Vectors 2. Recp of vectors Vectors re directed line segments - they cn be represented in component form or by direction nd mgnitude. We cn use trigonometry nd Pythgors theorem to switch between the forms
More informationEnterprise Data Center A c h itec tu re Consorzio Operativo Gruppo MPS Case S t u d y : P r o g et t o D i sast er R ec o v er y Milano, 7 Febbraio 2006 1 Il G r u p p o M P S L a B a n c a M o n t e d
More informationMatrices in Computer Graphics
Marce n Compuer Graphc Tng Yp Mah 8A // Tng Yp Mah 8A Abrac In h paper, we cu an eplore he bac mar operaon uch a ranlaon, roaon, calng an we wll en he cuon wh parallel an perpecve vew. Thee concep commonl
More informationDynamic Modeling of a Generalized Stewart Platform by Bond Graph Method Utilizing a Novel Spatial Visualization Technique
eol eew of ehl ee... ol.. D oel of eele Sew Plfo Bo ph eho Ul Noel Spl slo ehqe Đh Yılı sf. Öülü Ahe Sğılı As hs ppe epeses oel of eele sew plfo plo Bo ph eho wh ew spl slo eho he se-spe epeseo of he eqos
More informationWhen prices hardly matter: Incomplete insurance contracts and markets for repair goods
When res hrdly er: Inolee nsurne onrs nd rkes for rer goods Mrn Nell Professor of Rsk nd Insurne Unversy of Hurg, Gerny hone: 49 40 4838404, fx: 49 40 48385505 rn.nell@rrz.un-hurg.de Andres Rher Asssn
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationAngles 2.1. Exercise 2.1... Find the size of the lettered angles. Give reasons for your answers. a) b) c) Example
2.1 Angles Reognise lternte n orresponing ngles Key wors prllel lternte orresponing vertilly opposite Rememer, prllel lines re stright lines whih never meet or ross. The rrows show tht the lines re prllel
More informationR e t r o f i t o f t C i r u n i s g e C o n t r o l
R e t r o f i t o f t C i r u n i s g e C o n t r o l VB Sprinter D e s c r i p t i o n T h i s r e t r o f i t c o n s i s t s o f i n s t a l l i n g a c r u i s e c o n t r o l s wi t c h k i t i n
More informationThree-Phase Induction Generator Feeding a Single-Phase Electrical Distribution System - Time Domain Mathematical Model
Three-Phse Induton Genertor Feedng Sngle-Phse Eletrl Dstruton System - Tme Domn Mthemtl Model R.G. de Mendonç, MS. CEFET- GO Jtí Deentrlzed Unty Eletrotehnl Coordnton Jtí GO Brzl 763 L. Mrtns Neto, Dr.
More informationEM EA. D is trib u te d D e n ia l O f S e rv ic e
EM EA S e c u rity D e p lo y m e n t F o ru m D e n ia l o f S e rv ic e U p d a te P e te r P ro v a rt C o n s u ltin g S E p p ro v a rt@ c is c o.c o m 1 A g e n d a T h re a t U p d a te IO S Es
More informationOblique incidence: Interface between dielectric media
lecrmagnec Felds Oblque ncdence: Inerface beween delecrc meda Cnsder a planar nerface beween w delecrc meda. A plane wave s ncden a an angle frm medum. The nerface plane defnes he bundary beween he meda.
More informationCHAPTER 31 CAPACITOR
. Given tht Numer of eletron HPTER PITOR Net hrge Q.6 9.6 7 The net potentil ifferene L..6 pitne v 7.6 8 F.. r 5 m. m 8.854 5.4 6.95 5 F... Let the rius of the is R re R D mm m 8.85 r r 8.85 4. 5 m.5 m
More informationMORE ON TVM, "SIX FUNCTIONS OF A DOLLAR", FINANCIAL MECHANICS. Copyright 2004, S. Malpezzi
MORE ON VM, "SIX FUNCIONS OF A DOLLAR", FINANCIAL MECHANICS Copyrgh 2004, S. Malpezz I wan everyone o be very clear on boh he "rees" (our basc fnancal funcons) and he "fores" (he dea of he cash flow model).
More informationThe remaining two sides of the right triangle are called the legs of the right triangle.
10 MODULE 6. RADICAL EXPRESSIONS 6 Pythgoren Theorem The Pythgoren Theorem An ngle tht mesures 90 degrees is lled right ngle. If one of the ngles of tringle is right ngle, then the tringle is lled right
More informationPC Problems HelpDesk Service Agreement
Enn SS 7 b aw f Un Sa & anaa an b nnana a I IS ILLEGL ND SRILY ROHIIED O DISRIUE, ULISH, OFFER FOR SLE, LIENSE OR SULIENSE, GIVE OR DISLOSE O NY OHER RY, HIS RODU IN HRD OY OR DIGIL FORM LL OFFENDERS WILL
More informationEuroFGI Workshop on IP QoS and Traffic Control TITOLO. A Receiver Side Approach for Real-Time Monitoring of IP Performance Metrics
EuroFGI Workhop on IP QoS n Trff Conrol TITOLO A Rvr S Approh for Rl-T Monorng of IP Prforn Mr TESI R. G. Grroppo, S. Gorno, F. Oppno, G. Pro Dp. of Inforon Engnrng Unvry of P 1 Lbon, Porugl, Dbr 6-7,
More informationAN EVALUATION OF SHORT TERM TREATMENT PROGRAM FOR PERSONS DRIVING UNDER THE INFLUENCE OF ALCOHOL 1978-1981. P. A. V a le s, Ph.D.
AN EVALUATION OF SHORT TERM TREATMENT PROGRAM FOR PERSONS DRIVING UNDER THE INFLUENCE OF ALCOHOL 1978-1981 P. A. V a le s, Ph.D. SYNOPSIS Two in d ep en d en t tre a tm e n t g ro u p s, p a r t ic ip
More informationVictims Compensation Claim Status of All Pending Claims and Claims Decided Within the Last Three Years
Claim#:021914-174 Initials: J.T. Last4SSN: 6996 DOB: 5/3/1970 Crime Date: 4/30/2013 Status: Claim is currently under review. Decision expected within 7 days Claim#:041715-334 Initials: M.S. Last4SSN: 2957
More informationC o a t i a n P u b l i c D e b tm a n a g e m e n t a n d C h a l l e n g e s o f M a k e t D e v e l o p m e n t Z a g e bo 8 t h A p i l 2 0 1 1 h t t pdd w w wp i j fp h D p u b l i c2 d e b td S t
More informationGenerator stability analysis - Fractional tools application
Generor by ny - Frcon oo ppcon Auhor : Ocvn ENACHEANU Dephne RIU Nco RETIERE SDNE Grenobe -67 Oune. Eecrc nework cone. Frcon moeng o ynchronou mchne. Se pce repreenon n by conon o ynchronou mchne neger
More informationMr. Kepple. Motion at Constant Acceleration 1D Kinematics HW#5. Name: Date: Period: (b) Distance traveled. (a) Acceleration.
Moion Consn Accelerion 1D Kinemics HW#5 Mr. Kepple Nme: De: Period: 1. A cr cceleres from 1 m/s o 1 m/s in 6.0 s. () Wh ws is ccelerion? (b) How fr did i rel in his ime? Assume consn ccelerion. () Accelerion
More informationn Using the formula we get a confidence interval of 80±1.64
9.52 The professor of sttistics oticed tht the rks i his course re orlly distributed. He hs lso oticed tht his orig clss verge is 73% with stdrd devitio of 12% o their fil exs. His fteroo clsses verge
More informationEXAMPLE 1... 1 EXAMPLE 2... 14 EXAMPLE 3... 18 EXAMPLE 4 UNIVERSAL TRADITIONAL APPROACH... 24 EXAMPLE 5 FLEXIBLE PRODUCT... 26
EXAMLE... A. Edowme... B. ure edowme d Term surce... 4 C. Reseres... 8. Bruo premum d reseres... EXAMLE 2... 4 A. Whoe fe... 4 B. Reseres of Whoe fe... 6 C. Bruo Whoe fe... 7 EXAMLE 3... 8 A.ure edowme...
More informationThe Euro. Optimal Currency Areas. The Problem. The Euro. The Proposal. The Proposal
The Euro E Opial Currency Areas ( σ ( r The Euro is an exaple of a currency union. The naions abandoned independen oneary auhoriy o ge a coon currency. Lecures in Macroeconoics- Charles W. Upon Opial Currency
More informationSolution ----------------------------------------------------------------------------------------- y y = 0 = 0.0204 = 0.250
Chper 5 Exmple 5.2-2. 6 ---------------------------------------------------------------------------------- r ower i o e deigned o or SO 2 from n ir rem uing pure wer 20 o C. The enering g conin 20 mol
More information1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z
o ffix uden abel ere uden ame chool ame isric ame/ ender emale ale onh ay ear ae of irh an eb ar pr ay un ul ug ep c ov ec as ame irs ame lace he uden abel ere ae uden denifier chool se nly rined in he
More information. At first sight a! b seems an unwieldy formula but use of the following mnemonic will possibly help. a 1 a 2 a 3 a 1 a 2
7 CHAPTER THREE. Cross Product Given two vectors = (,, nd = (,, in R, the cross product of nd written! is defined to e: " = (!,!,! Note! clled cross is VECTOR (unlike which is sclr. Exmple (,, " (4,5,6
More informationPHYSICS 161 EXAM III: Thursday December 04, 2003 11:00 a.m.
PHYS 6: Eam III Fall 003 PHYSICS 6 EXAM III: Thusda Decembe 04, 003 :00 a.m. Po. N. S. Chan. Please pn ou name and ene ou sea numbe o den ou and ou eamnaon. Suden s Pned Name: Recaon Secon Numbe: Sea Numbe:.
More informationWhen prices hardly matter: Incomplete insurance contracts and markets for repair goods
Mrn Nell, Andres Rher, Jörg Shller When res hrdly er: Inolee nsurne onrs nd rkes for rer goods Workng Pers on Rsk nd Insurne Hurg Unversy No 4 Jnury 005 Tor zur Wel der Wssenshf Mrn Nell, Andres Rher,
More informationSecure Hash Standard (SHS) The 8/2015 release of FIPS 180-4 updates only the Applicability Clause. Final Publication of FIPS 180-4:
The ched drf FIPS 8- provded here for hsorcl purposes hs been superseded by he followng FIPS publcon: Publcon Number: FIPS 8- Tle: Secure sh Sndrd SS Publcon De: 8/5 The 8/5 relese of FIPS 8- updes only
More informationEQUATIONS OF LINES AND PLANES
EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint
More information1.- L a m e j o r o p c ió n e s c l o na r e l d i s co ( s e e x p li c a r á d es p u é s ).
PROCEDIMIENTO DE RECUPERACION Y COPIAS DE SEGURIDAD DEL CORTAFUEGOS LINUX P ar a p od e r re c u p e ra r nu e s t r o c o rt a f u e go s an t e un d es a s t r e ( r ot u r a d e l di s c o o d e l a
More information5.6 POSITIVE INTEGRAL EXPONENTS
54 (5 ) Chpter 5 Polynoils nd Eponents 5.6 POSITIVE INTEGRAL EXPONENTS In this section The product rule for positive integrl eponents ws presented in Section 5., nd the quotient rule ws presented in Section
More informationSCO TT G LEA SO N D EM O Z G EB R E-
SCO TT G LEA SO N D EM O Z G EB R E- EG Z IA B H ER e d it o r s N ) LICA TIO N S A N D M ETH O D S t DVD N CLUDED C o n t e n Ls Pr e fa c e x v G l o b a l N a v i g a t i o n Sa t e llit e S y s t e
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More informationSection 7-4 Translation of Axes
62 7 ADDITIONAL TOPICS IN ANALYTIC GEOMETRY Section 7-4 Trnsltion of Aes Trnsltion of Aes Stndrd Equtions of Trnslted Conics Grphing Equtions of the Form A 2 C 2 D E F 0 Finding Equtions of Conics In the
More informationTHEORETICAL STUDY ON PIPE OF TAPERED THICKNESS WITH AN INTERNAL FLOW TO ESTIMATE NATURAL FREQUENCY
Inernaonal Journal of Mechancal Engneerng and Technology (IJMET) Volue 7, Issue, March-Arl 6,., Arcle ID: IJMET_7 Avalable onlne a h://www.aee.co/ijmet/ssues.as?jtye=ijmet&vtye=7&itye= Journal Iac Facor
More informationU S B Pay m e n t P r o c e s s i n g TM
U S B Pay m e n t P r o c e s s i n g T h a t s S m a r t P r o c e s s i n g TM USB was simple to enroll in. They had competitive rates and all the fees were listed clearly with no surprises. Everyone
More informationRatio and Proportion
Rtio nd Proportion Rtio: The onept of rtio ours frequently nd in wide vriety of wys For exmple: A newspper reports tht the rtio of Repulins to Demorts on ertin Congressionl ommittee is 3 to The student/fulty
More informationPROBLEMS 05 - ELLIPSE Page 1
PROBLEMS 0 ELLIPSE Pge 1 ( 1 ) The edpoits A d B of AB re o the X d Yis respectivel If AB > 0 > 0 d P divides AB from A i the rtio : the show tht P lies o the ellipse 1 ( ) If the feet of the perpediculrs
More informationOverview of Spellings on www.spellzoo.co.uk
Overview of Spellings on www.spellzoo.co.uk Year 1 Set 1: CVC words Set 2: CVC and CCVC words Set 3: CVC, CCVC and CCVCC words Set 4: Words containing 'ch', 'sh', 'th' and 'wh' Set 5: Words ending in 'll',
More informationMathematics. Vectors. hsn.uk.net. Higher. Contents. Vectors 128 HSN23100
hsn.uk.net Higher Mthemtics UNIT 3 OUTCOME 1 Vectors Contents Vectors 18 1 Vectors nd Sclrs 18 Components 18 3 Mgnitude 130 4 Equl Vectors 131 5 Addition nd Subtrction of Vectors 13 6 Multipliction by
More informationm Future of learning Zehn J a hr e N et A c a d ei n E r f o l g s p r o g r a m Cisco E x p o 2 0 0 7 2 6. J u n i 2 0 0 7, M e sse W ie n C. D or n in g e r, b m u k k 1/ 12 P r e n t t z d e r p u t
More informationDer Bologna- P roz es s u nd d i e S t aat s ex am Stefan Bienefeld i na Service-St el l e B o l o g n a d er H R K Sem in a r D er B o l o g n a P ro z es s U m s et z u n g u n d M it g es t a l t u
More informationHR DEPARTMENTAL SUFFIX & ORGANIZATION CODES
HR DEPARTMENTAL SUFFIX & ORGANIZATION CODES Department Suffix Organization Academic Affairs and Dean of Faculty, VP AA 1100 Admissions (Undergraduate) AD 1330 Advanced Ceramics, Colorado Center for--ccac
More informationRC (Resistor-Capacitor) Circuits. AP Physics C
(Resisor-Capacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College - Physics 2426 - Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationI n la n d N a v ig a t io n a co n t r ib u t io n t o eco n o m y su st a i n a b i l i t y
I n la n d N a v ig a t io n a co n t r ib u t io n t o eco n o m y su st a i n a b i l i t y and KB rl iak s iol mi a, hme t a ro cp hm a5 a 2k p0r0o 9f i,e ls hv oa nr t ds eu rmv oedye l o nf dae cr
More informationImproper Integrals. Dr. Philippe B. laval Kennesaw State University. September 19, 2005. f (x) dx over a finite interval [a, b].
Improper Inegrls Dr. Philippe B. lvl Kennesw Se Universiy Sepember 9, 25 Absrc Noes on improper inegrls. Improper Inegrls. Inroducion In Clculus II, sudens defined he inegrl f (x) over finie inervl [,
More informationPermutations and Combinations
Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes - ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he k-value for he middle erm, divide
More informationSECURE E-MAIL USER GUIDE FOR EXTERNAL PARTNERS
SECURE E-MAIL USER GUIDE FOR EXTERNAL PARTNERS A guide for using encrypted electronic mail to protect the privacy and data integrity of sensitive information. August 2014 Data Classification: Public Information
More informationB I N G O B I N G O. Hf Cd Na Nb Lr. I Fl Fr Mo Si. Ho Bi Ce Eu Ac. Md Co P Pa Tc. Uut Rh K N. Sb At Md H. Bh Cm H Bi Es. Mo Uus Lu P F.
Hf Cd Na Nb Lr Ho Bi Ce u Ac I Fl Fr Mo i Md Co P Pa Tc Uut Rh K N Dy Cl N Am b At Md H Y Bh Cm H Bi s Mo Uus Lu P F Cu Ar Ag Mg K Thomas Jefferson National Accelerator Facility - Office of cience ducation
More informationVolumes by Cylindrical Shells: the Shell Method
olumes Clinril Shells: the Shell Metho Another metho of fin the volumes of solis of revolution is the shell metho. It n usull fin volumes tht re otherwise iffiult to evlute using the Dis / Wsher metho.
More informationThuraya XT-LITE Simple. Reliable. Affordable.
Thuraya XT-LITE Simple. Reliable. Affordable. www.thuraya.com Follow us on /thurayatelecom Stayi n g c on n ec ted has n ever b een thi s eas y. In trodu c i n g T hu raya X T -LIT E, the wo r l d s be
More informationW Cisco Kompetanse eek end 2 0 0 8 SMB = Store Mu ll ii gg hh eter! Nina Gullerud ng ulleru@ c is c o. c o m 1 Vår E n t e r p r i s e e r f a r i n g... 2 S m å o g M e llo m s t o r e B e d r i f t e
More informationProduct catalogue. Steel in ingots
Prouct ctlogue Steel in ingots Grup lchemi Prouct ctlogue ut tory elonging to lchemi Cpitl Group is one of the Europen mjor proucers of top qulity lrge imeter semless steel pipes (rnge: from 219 mm to
More information4 Convolution. Recommended Problems. x2[n] 1 2[n]
4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.
More informationPut the human back in Human Resources.
Put the human back in Human Resources A Co m p l et e Hu m a n Ca p i t a l Ma n a g em en t So l u t i o n t h a t em p o w er s HR p r o f essi o n a l s t o m eet t h ei r co r p o r a t e o b j ect
More informationREVISTA INVESTIGACION OPERACIONAL Vol. 25, No. 1, 2004. k n ),
REVISTA INVESTIGACION OPERACIONAL Vol 25, No, 24 RECURRENCE AND DIRECT FORMULAS FOR TE AL & LA NUMBERS Eduardo Pza Volo Cero de Ivesgacó e Maemáca Pura y Aplcada (CIMPA), Uversdad de Cosa Rca ABSTRACT
More informationCOMPLEX FRACTIONS. section. Simplifying Complex Fractions
58 (6-6) Chpter 6 Rtionl Epressions undles tht they cn ttch while working together for 0 hours. 00 600 6 FIGURE FOR EXERCISE 9 95. Selling. George sells one gzine suscription every 0 inutes, wheres Theres
More informationOnline Department Stores. What are we searching for?
Online Department Stores What are we searching for? 2 3 CONTENTS Table of contents 02 Table of contents 03 Search 06 Fashion vs. footwear 04 A few key pieces 08 About SimilarWeb Stepping up the Competition
More informationThe art of Paperarchitecture (PA). MANUAL
The rt of Pperrhiteture (PA). MANUAL Introution Pperrhiteture (PA) is the rt of reting three-imensionl (3D) ojets out of plin piee of pper or ror. At first, esign is rwn (mnully or printe (using grphil
More informationSINCLAIR COMMUNITY COLLEGE DAYTON, OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 1355 - INTERMEDIATE ALGEBRA I (3 CREDIT HOURS)
SINCLAIR COMMUNITY COLLEGE DAYTON OHIO DEPARTMENT SYLLABUS FOR COURSE IN MAT 1355 - INTERMEDIATE ALGEBRA I (3 CREDIT HOURS) 1. COURSE DESCRIPTION: Ftorig; opertios with polyoils d rtiol expressios; solvig
More informationBLADE 12th Generation. Rafał Olszewski. Łukasz Matras
BLADE 12th Generation Rafał Olszewski Łukasz Matras Jugowice, 15-11-2012 Gl o b a l M a r k e t i n g Dell PowerEdge M-Series Blade Server Portfolio M-Series Blades couple powerful computing capabilities
More informationLECTURE #05. Learning Objective. To describe the geometry in and around a unit cell in terms of directions and planes.
LECTURE #05 Chpter 3: Lttice Positions, Directions nd Plnes Lerning Objective To describe the geometr in nd round unit cell in terms of directions nd plnes. 1 Relevnt Reding for this Lecture... Pges 64-83.
More informationImagine a Source (S) of sound waves that emits waves having frequency f and therefore
heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing
More informationH ig h L e v e l O v e r v iew. S te p h a n M a rt in. S e n io r S y s te m A rc h i te ct
H ig h L e v e l O v e r v iew S te p h a n M a rt in S e n io r S y s te m A rc h i te ct OPEN XCHANGE Architecture Overview A ge nda D es ig n G o als A rc h i te ct u re O ve rv i ew S c a l a b ili
More information( ) Ú Ú. Ú Ú, c is a constant Ú Ú Ú Ú Ú. a Ú for any value of c. Ú Ú Ú Ú Ú Ú Ú ( ) =- ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
Definie Inegrl: Suppose f on [, ]. Divie [, ] wih D n hoose Clulus Che Shee Inegrls Definiions is oninuous ino n suinervls of from eh inervl. * i * Then limâ ( i ) f = f D. næ i = AniDerivive : An nierivive
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More information<?xml version="1.0" encoding="utf-8"?> <soapenv:envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/"
Applicazioni Java W S con Ax is sistema di tr ac c iab il ità ag r o al imen tar e Ing. Mario G.C.A. Cimino M.G.C.A.Cimino, Applicazioni Java-W S con Ax is, D ipar t ime nt o d i I ng e g ne r ia d e ll
More informationSummary: Vectors. This theorem is used to find any points (or position vectors) on a given line (direction vector). Two ways RT can be applied:
Summ: Vectos ) Rtio Theoem (RT) This theoem is used to find n points (o position vectos) on given line (diection vecto). Two ws RT cn e pplied: Cse : If the point lies BETWEEN two known position vectos
More informationEnd of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.
End of term: TEST A You will need penil nd ruler. Yer Nme Clss Dte Complete the missing numers in the sequenes elow. 8 30 3 28 2 9 25 00 75 25 2 Put irle round ll of the following shpes whih hve 3 shded.
More informations in? sure? not dufferinwaste Try searching the What Goes Where directory, available at dufferincounty.ca/waste or on the my-wastetm app
s? Try searg e Wa Ges Were rery, avalale a ffery.a/ase r e my-asetm a EMPTY PANT CAN BLUE BOX Te keyr ere s emy. f y fs a a f a, js leave e l ff fr a fe ays le ry. Te a a e l a g e Ble Bx searaely. f y
More informationOutline. Numerical Analysis Boundary Value Problems & PDE. Exam. Boundary Value Problems. Boundary Value Problems. Solution to BVProblems
Oulie Numericl Alysis oudry Vlue Prolems & PDE Lecure 5 Jeff Prker oudry Vlue Prolems Sooig Meod Fiie Differece Meod ollocio Fiie Eleme Fll, Pril Differeil Equios Recp of ove Exm You will o e le o rig
More informationHow To Find The Re Of Tringle
Heron s Formul for Tringulr Are y Christy Willims, Crystl Holom, nd Kyl Gifford Heron of Alexndri Physiist, mthemtiin, nd engineer Tught t the museum in Alexndri Interests were more prtil (mehnis, engineering,
More information17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides
7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion
More informationB A S I C S C I E N C E S
B A S I C S C I E N C E S 10 B A S I C S C I E N C E S F I R S T S E M E S T E R C O U R S E S : H U M A N S T R U C T U R E A N D F U N C T I O N [ H S F I ] M O L E C U L A R B A S I S O F M E D I C
More informationMATH PLACEMENT REVIEW GUIDE
MATH PLACEMENT REVIEW GUIDE This guie is intene s fous for your review efore tking the plement test. The questions presente here my not e on the plement test. Although si skills lultor is provie for your
More information1 Fractions from an advanced point of view
1 Frtions from n vne point of view We re going to stuy frtions from the viewpoint of moern lger, or strt lger. Our gol is to evelop eeper unerstning of wht n men. One onsequene of our eeper unerstning
More informationChem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry
Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Why? Chemists are concerned with mass relationships in chemical reactions, usually run on a macroscopic scale (grams, kilograms, etc.). To deal with
More information