$2.$ Pitching and Rolling Moment Coefficients $-$ Assume a conventional fixed$-$wing aircraft $($general aviation$)$ with a positive wing dihedral.

a$.$ Determine the sign of the elevator control derivative $\backslash ($ C$\_\{$m$\_\{\backslash$delta$\_\{$e$\}\}\}\backslash )$ and briefly explain your reasoning. In your explanation, include a free$-$body diagram showing the appropriate frame of reference, the center of gravity $($CG$),$ the elevator aerodynamic center, and the forces and moments acting on both the elevator and at the CG$.$

b$.$ Explain how the positive dihedral angle of the wing affects the rolling moment coefficient due to sideslip, $\backslash ($ C$\_\{$l$\_\{\backslash$beta$\}\}\backslash ).$ Provide a brief justification and support your explanation with a sketch that illustrates the dihedral's effect.