Question 18Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.F = (x² + y2)i + (x - y)j; C is the rectangle with vertices at (0, 0), (2, 0), (2, 9), and (0, 9)0180144-144

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Answered: Using Green's Theorem, compute the…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 11P

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#23
Linear Algebra - Linear Transformation Defn.: A function T: V→W is one-to-one (injective) if T(x1)=T(x2) implies x1=x2. T is onto (surjective) if T(V)=W. Let T: R3 → R2 defined by T(x,y,z)=(x+2y+3z, x-y). Is T one-to-one? Is T onto? Provide prove for both.
Z z+1 == The inverse image of the disk | z | <²1/ under T(z) is
(b) Use Green's theorem to calculate the circulation of F around the triangle with verticcs (2, 0), (0, 3), (–2,0) oricntcd counterclockwisc where F = (2x²+3y)i+ (2.x + 3y²)j.
Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F = (x - y)i + (x + y)j; C is the triangle with vertices at (0, 0), (2, 0), and (0,4) 32 8 0 16
D. Please help me with this math. Image attached. Thank you.
Write f(z) in polar form f(2)= u(r,0)+iv(r,0). f(2)=z² +42²-6
Use Green's Theorem to find the counterclockwise circulation of F around the closed curve C. F=(x²+y²)i+(x-y)j; C is the rectangle with vertices at (0,0), (2,0), (2,2), (0,2)
Subject: calculus
(3) Consider the linear map T : R² → R² which sends (1,0) → (-3, 5) and (0,1) → (4, –1). (a) What is the matrix of the transformation? What is the change of coordinates matrix? Do they agree? How come? (b) Where does this transformation send the area between the vector (4, 2) and the X-axis? Explain algebraically and draw a picture. (c) What is the image of the lower half plane under T? Explain algebraically and draw a picture. (d) What is the pre-image of the upper half plane under T? Explain algebraically and draw a picture. (e) What is the image of the unit circle under T? Explain algebraically and draw a picture. (f) Deduce whether or not linear transformations preserve angles/areas/curves/shapes, 6, etc.
K- Use the flux form of Green's Theorem to evaluate (exy+By³) dA, where R is the triangle with vertices (0,0). (1.0), and (0.1). (8xy + 8y³) dA= R (Simplify your answer.) R SOOD
17

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Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F = (x² + y2)i + (x - y)j; C is the rectangle with vertices at (0, 0), (2, 0), (2, 9), and (0, 9) 0 180 144 -144