Find positive numbers $a$ and $b$ so that the change of variables $s=ax, t=by$ transforms the integral $\int\int_R \,dx\,dy$ into $$\int\int_T \left\vert \frac{\partial(x,y)}{\partial(s,t)}\right\vert\,ds\,dt$$ for the region $R$, the elliptical region $x^2/9 + y^2/16\le 1$ and the region $T$, the circle $s^2 + t^2 = 1$.

$a =$
$b =$

What is $\left\vert \frac{\partial(x,y)}{\partial(s,t)}\right\vert$ in this case?
$\left\vert \frac{\partial(x,y)}{\partial(s,t)}\right\vert =$