WeBWorK Standalone Renderer

Suppose a change of coordinates $T : \mathbb{R}^2 \to \mathbb{R}^2$ from the $uv$ -plane to the $xy$ -plane is given by

$x = v-3u+5, \ \ \ y = -3-3u+3v.$
(a) Find the absolute value of the determinant of the Jacobian for this change of coordinates.

$\displaystyle \left| \frac{\partial(x,y)}{\partial(u,v)} \right| = \bigg| \mathrm{det}$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$			$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

$\bigg| =$

(b) If a region $D^*$ in the $uv$ -plane has area $7.36$ , find the area of the region $T(D^*)$ in the $xy$ -plane.

Area =

You can earn partial credit on this problem.