Problem $7$: upside$-$down airfoil $($BONUS $+10$ pts$).$ A question is often asked: Can an airfoil fly upside$-$down? To answer this, make the following calculation. Consider a positively cambered airfoil with a zero$-$lift angle of $\backslash (-3^\{\backslash$circ$\}\backslash ).$ The lift slope is $0\mathrm{.}1$ per degree. Consider only the linear section of $\backslash ($ c$\_\{$l$\}\backslash )$ vs$.\backslash (\backslash$alpha $\backslash )$ relationship in this problem.

$($a$)(2$ pts$)$ Calculate the lift coefficient at an angle of attack of $\backslash (5^\{\backslash$circ$\}\backslash ).$

$($b$)(4$ pts$)$ Now imagine the same airfoil turned upside$-$down, but at the same $\backslash (5^\{\backslash$circ$\}\backslash )$ angle of attack as the previous part. Calculate the lift coefficient.

$($c$)(4$ pts$)$ At what angle of attack must the upside$-$down airfoil be set to generate the same lift as that when it is right$-$side$-$up at a $\backslash (5^\{\backslash$circ$\}\backslash )$ angle of attack?