$(15\%)$ For a two$-$dimensional flow field, the $x$ and the $y$ velocity components are given by $u=3x^2-3y^2$ and $v=-6xy($unit: $\frac{m}{s}),$ respectively. Please answer the following questions:

$($a$)$ Is it an incompressible flow? And why?

$($b$)$ Find the stream function for it$,$ if it is incompressible flow.

$($c$)$ Is the flow irrotational? And why?

$($d$)$ If this is irrotational flow, please find the velocity potential function for it$.$