This is a slightly specific question but I'm not sure how to even begin or go about doing it:

Find a bijection from a closed disk:

$D=\{(x,y)\in\mathbb{R}^2|x^2+y^2\leq 1\}$

To the open square:

$S = (0,1) \times (0,1)=\{(x,y)\in \mathbb{R}^2|0<x<1, 0<y<1\}$