Use the liner transformation T: (u, v) → (x, y) given by 1 1 T(u, v) = (-u + v)i + ÷(u+ 3v)j 4 4 to rewrite the integral 4.x – 8y dA where R is the triangular region with vertices (0,0), (1, 3) and (4,0).

Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

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Q: (z-i)² 2. Show that the transformation w = maps the interior of the semicircle |z| = 1 into (z+i)²…

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Q: Find the Jacobian J of the transformation T(u, v, w) = (-3u +5v-3w, 2u+4v+3w, 4u+v=4w) = (x, y, z).…

A: Given:- Tu,v,w=-3u+5v-3w,2u+4v+3w,4u+v-4w=x,y,z

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

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Q: SLo(xy) dA where R is bounded by 9x2 + 4y² = 36 %3D Use the transformation: x = 2u and y = 3v

A: The given region R is: 9x2+4y2=36...(1) To use the transformation: x=2u,y=3v So, equation (1)…

Q: Consider the following Linear Transformation to change coordinates for a double in parallelogram: U…

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Q: Q3: Evaluate z+ 2ydA where R is the triangle with vertices (0,3), (4, 1) and (2, 6) 1 1 using the…

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Q: a(x,y) Let G(u, v) = (5u + 2v, 5u+9v) be a map from the uv-plane to the xy-plane. Calculate Jac(G) =…

A: Given that be a map from the -plane to the -plane.The objective is to calculate .

Q: 12. Use the transformation z (u + v), y = (v - 3u) to evaluate the integral ff (4x+8y) dA, where R…

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Q: Nedd help with d)

A: (d) To determine if the given mapping T is a linear transformation on the plane R^2

Q: let T. R²₁ R² Such that T(x, y) = (2x + y²₁ y=x), Show That Tis linear Transformation.

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Q: the Jacobian of the transformation. x = 6u + 5v,    y = 7u + 2v  ∂(x, y) ∂(u, v

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Q: Q4 Evaluate S SR (x + 2y) dA where R is the triangle with the vertices (0, 3).(4, 1) and (2,6) using…

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Q: Explain how to compute the Jacobian of the transformationT: x = g(u, v), y = h(u, v).

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Q: Evaluate the Jacoblain Jlu,v, w) for the transformatión : X = VW , y= Ww %3D

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Q: CD has coordinates C(-8,-2) and D(-4,-12). determine the coordiantes of C'D' if (x,y) -> (1/2x,1/2y)…

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Q: Use the transformation u=-2.= 3y and =z to evaluate (5- Sy) de dzdy.

A: Introduction: The process of determining the area of the region under the curve is known as…

Q: Find a transformation that таps R = {z = x + iy : x > 2, y > 1} onto S = {z = x + iy : x < -1, y…

A: We need to find a transformation that maps R = { z = x+iy : x ≥ 2, y ≥ 1} onto S = { z = x+iy : x ≤…

Q: Evaluate S (x + y)dxdy, where R is the trapezoidal domain with vertices given by (0,0), (5,0), (5/2,…

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Q: Find the image of the semi-infinite strip x 2 5,2 < y < 6 in the z - plane under the transformation…

A: Use the equations of complex numbers and imaginary numbers to simplify the given expressions and…

Q: Do not use any spaces when you input your coordinates Tis the shear represented by the linear…

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