$(40$ pts$)$ A steady two$-$dimensional flow in the $x-y$ plane has velocity field

vec$(V)=(2\mathrm{.}20+5\mathrm{.}60x+1\mathrm{.}30y)vec(i)+(1\mathrm{.}96-4\mathrm{.}20x-5\mathrm{.}60y)vec(j)$

Do not concern yourself with units $-$ assume that the constants have appropriate units for dimensional consistency.

$($a$)$ Calculate the acceleration field and give your answer as the components $a_x$ and $a_y.$

$($b$)$ Calculate the acceleration at the point $(x,y)=(-2,3).$

$($c$)$ Is this flow incompressible? Show why or why not.

$($d$)$ Is this flow irrotational? Show why or why not.

$($e$)$ Calculate all nine components of the strain rate tensor at this location and show your result as a $33$ matrix in the usual

fashion. Are the $x-y$ axes principal axes? Why or why not?