Problem $1.(50$ points$)$ Consider a velocity field with

$u=5t^4$

$v=e^{-2t}+11x^2$

$($a$)$ Show that mass is conserved for an incompressible flow.

$($b$)$ Find the streamline that path through point $(1,1)$ at different times.

$($c$)$ Determine the path line of a particle that starts at $(1,1)$ at time $t=0.$

$($d$)$ Find the streak line of point $(1,1)$ at time $1.$

$($d$)$ Evaluate the deformation rate tensor.