Consider the transformation $T: x = \frac{12}{37}u - \frac{35}{37}v, \ \ y = \frac{35}{37}u + \frac{12}{37}v$

A. Compute the Jacobian:
$\frac{\partial(x, y)}{\partial(u, v)} =$

B. The transformation is linear, which implies that it transforms lines into lines. Thus, it transforms the square $S:-37 \leq u \leq 37, -37 \leq v \leq 37$ into a square $T(S)$ with vertices:

T(37, 37) = (, )

T(-37, 37) = (, )

T(-37, -37) = (, )

T(37, -37) = (, )

C. Use the transformation $T$ to evaluate the integral $\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}$