$(1$ point$)$ Let $S$ be an opened cylindrical can standing on the $xy-$plane. $(S$ has a bottom and sides, but no top.$)$ The side of $S$ is given by $x^2+y^2=4,$ and its height is $3.$

$($a$)$ Give a parametric equation, vec$(r)(t)$ for the rim, $C$

vec$(r)(t)=$

$$ with $,t$

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

$($b$)$ If $S$ is oriented outward and downward, find

${\displaystyle \underset{S}{\overset{\phantom{}}{}}}(grad(-7$yvec$(i)+7$xvec$(j)+5$zvec$(k)))*dvec(A)$

${\displaystyle \underset{S}{\overset{\phantom{}}{}}}(grad(-7$yvec$(i)+7$xvec$(j)+5$zvec$(k)))*dvec(A)=$