The figure below open cylindrical can, $S,$ standing on the $xy-$plane. $(S$ has a bottom and sides, but no top.$)$

The side of $S$ is given by $x^2+y^2=1,$ and its height is $3.$

$($a$)$ Give a parametric equation, $r(t)$ for the rim, $C.($In other words, $C$ is the circle at the top of the cylinder.$)$

$r(t)=,$ with $,t$

$($For this problem, enter your vector equation with angle$-$bracket notation: $.)$

$($b$)$ If $S$ is oriented outward and downward, find ${}_S$curl$(-3yi+3xj+7zk)*dS.$

${}_S$curl$(-3yi+3xj+7zk)*dS=$