A $900-$mm$-$wide, $24-$mm$-$thick annealed aluminum alloy strip is fed through a rolling mill with two powered rolls each with a radius of $280$ mm$.$ The annealed aluminum alloy has a strength coefficient K of $205$ MPa and a strain hardening exponent n of $0\mathrm{.}20.$ The strip thickness is to be reduced to $18$ mm in one pass with a roll speed of $30$ rpm$.$ Assume that the strip is fully engaged between the rolls and that the rolling pressure can be calculated as the average flow stress in plane strain of the material in the roll gap. Calculate $($a$)$ the length of contact between the roll and the strip $[$mm$],($b$)$ the rolling force $[$MN$],($c$)$ the torque driving each roll $[$MN$$m$],$ and $($d$)$ the total power required for this operation $[$MW$].$