Compute the Jacobian J(u,v) for the following transformation. T: x =20u cos (nv), y = 20u sin (V) Choose the correct Jacobian determinant of T below. A. J(u,v)= (20u cos (XV)) (20u sin (TV)) - (20u cos (xv)) (20u sin (xv)) d d d O B. J(u,v)= (20u sin (IV)-(20u cos (V)) - (20usin (nV)-(20u cos (IV)) O C. J(u,v) = (20u cos (XV)) (20u cos (xV)) - (20u sin (*v) (20u sin (IV)) d d O D. J(u,v) = =(20u sin (v)-(20u sin (IV) - (20u cos (TV)) (20u cos (IV)) Compute the Jacobian. J(u,v) =Solve the following relations for x and y, and compute the Jacobian J(u,v). U=xty, v= 2x - y X= y = (Type expressions using u and v as the variables.)\fLet S= {0 sus 1, 0Evs 1} be a unit square in the uv-plane. Find the image of S in the xy-plane under the following transformation. T: x = 5u, y= A V The image of S is the with vertices at]. (Type ordered pairs. U or any numbers in the expression. Use a comma to separate answers as needed.) diamond rectangle quarter circle triangle