$(10$ points$)$ For a flying wing configuration, the coefficient of moment about the aerodynamic center of the wing $C_{\text{m}\text{a}\text{c}\text{,}\text{w}\text{i}\text{n}\text{g}}=-0\mathrm{.}12$; the zero$-$angle lift coefficient $C_{L0,\text{w}\text{i}\text{n}\text{g}}=0\mathrm{.}37$; the location of aerodynamic center is ${\stackrel{}{x}}_{ac,\text{w}\text{i}\text{n}\text{g}}=0\mathrm{.}23$; the location of center of gravity is ${\stackrel{}{x}}_{cg}=0\mathrm{.}4$; and the rate of change of lift coefficient with respect to angle of attack $d\frac{C_L}{d}=5\mathrm{.}2$ per radian. Given this information

$($a$)$ Is the aircraft longitudinally stable?

$($b$)$ Can the aircraft be balanced?

$($c$)$ Plot $($using a plotting software$)C_{m,cg}$ vs $$

$($d$)$ If the aircraft can be balanced, find the trim angle of attack

$($e$)$ If not, make some suggestions to make the aircraft balanceable. Be as specific as possible