please ans me in 15 mins Consider the transformation x =p sin ф сos 0, у — р sin фsin @, z — рсos фfrom spherical to rectangular coordinates, where 0 < ¢ < T.Finda (x, y, z)о (р, ф, 0)p² sin oO p? cos oOp sin o

Given that: x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ

Answered: Consider the transformation a = p sin p…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.1: Introduction To Linear Transformations

Problem 46E: For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T...

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Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.
For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.
Consider the transformation x=r cos θ, y=r sin θ, z=z from cylinderical to rectangular coordinates,where r≥0. Find ∂(x, y, z)∂(r, θ, z). a) r b) −1 c) −r d) 1
Apply the transformation T (x, y) = (0.8x − 0.6y, 0.6x + 0.8y) to the scalene triangle whose vertices are (0, 0), (5, 0), and (0, 10). What kind of isometry does T seem to be? Be as specific as you can, and provide numerical evidence for your conclusion.
Let r(t)=⟨sin(t),cos(t),9sin(t)+3cos(2t)⟩. Find the projection of r(t)r(t) onto the xz-plane for −1≤x≤1.
Use the given transformation to evaluate the integral. (9x + 12y) dA R , where R is the parallelogram with vertices (−1, 2), (1, −2), (3, 0), and (1, 4); x = 1 3 (u + v), y = 1 3 (v − 2u)
Find the Jacobian of the transformation. x = 6u/v, y = 7v/w, z = 4w/u ∂(x, y, z) ∂(u, v, w) =
Use the given transformation to evaluate the integral. (15x + 15y) dA R , where R is the parallelogram with vertices (−1, 4), (1, −4), (3, −2), and (1, 6) ; x = 1/5(u + v), y =1/5(v − 4u)

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Consider the transformation a = p sin p cos 0, y = p sin ø sin 0, z = p cos ¢ from spherical to rectangular coordinates, where 0 < ¢ < T. Find a (x, y, z) a (p, ø, 0)