The rotating loop in an AC generator is a square $11\mathrm{.}0$ cm on a side. It is rotated at $90\mathrm{.}0$ Hz in a uniform field of $0\mathrm{.}800$ T$.$

Calculate the following quantities as functions of time t$,$ where t is in seconds.

$($a$)$ the flux through the loop

$(0\mathrm{.}00968-1$e$3)$ cos$(565-+)$ mT$-$m

$($b$)$ the emf induced in the loop

$(5\mathrm{.}47)$ sin$(565-+)$ V

$($c$)$ the current induced in the loop for a loop resistance of $2\mathrm{.}00$

$(2\mathrm{.}74)-$ sin$(565$ t$)$ A

$($d$)$ the power delivered to the loop

$(14\mathrm{.}98)($sin$(565-$ t$))?$ W

$($e$)$ the torque that must be exerted to rotate the loop