Consider the transformation T:x=(41/40)u−(9/41)v , y=(9/41)u+(40/41)v

Question

A. Computer the Jacobian:
delta(x,y)/delta(u,v)= ?

B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square S:−41<=u<=41, −41<=v<=41 into a square T(S) with vertices:

T(41, 41) = ( ? , ? )

T(-41, 41) = ( ? , ? )

T(-41, -41) = ( ? , ? )

T(41, -41) = ( ? , ? )

C. Use the transformation T to evaluate the integral double integral_T(S) (x^2+y^2) dA