$2\mathrm{.}4$ Consider the steady Cartesian velocity

vec$(u)=[\frac{-Ay}{(x^2+y^2{)}^{}},\frac{+Ax}{(x^2+y^2{)}^{}},0]$

a$)$ Determine the streamline that passes through $x=(x_o,y_o,0)$

b$)$ Compute $R_{ij}$ for this velocity field.

c$)$ For $A>0,$ explain the sense of rotation $($i$.$e$.$ clockwise or counter clockwise$)$ for

fluid elements for and $>1.$