Let $S=(D),$ where $D=\{(u,v)$:$u^2+v^{2}9,u0,v0\}$ and $(u,v)=(2u+1,u-v,3u+v).$

$($a$)$ Calculate the surface area of $S.$

$($Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

area$(S)=$

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$($b$)$ Evaluate ${}_S(4x-4y)dS.$

Hint: Use polar coordinates.

$($Express numbers in exact form. Use symbolic notation and fractions where needed.$)$

${}_S(4x-4y)dS=$

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