Consider a velocity field in $2$D given by:

vec$(V)=-$yhat$(i)+$xhat$(j)$

$($a$)$ Compute the velocity gradient tensor $(\frac{del{V}_i}{del{x}_j}).$

$($b$)$ Determine the strain rate tensor and the rotation rate tensor.

$($c$)$ Find the principal axes of the strain rate tensor by calculating its eigenvalues and eigenvectors.

$($d$)$ Explain the physical meaning of the principal axes for this flow field and comment on whether the flow

is purely rotational or deformational.