$(4$ points$)$

$($a$)$ Sketch a the vector field $F=yi+xj$ in the $xy-$plane.

$($b$)$ Based on your sketch, what is the direction of rotation of a thin twig placed at the origin along the $x-$axis?

$($c$)$ Based on your sketch, what is the direction of rotation of a thin twig placed at the origin along the $y-$axis?

$($d$)$ Compute curl$(F).$