$5.$ The Lockheed SR$-71$ Blackbird airplane currently holds the official Air Speed Record for a manned airbreathing jet aircraft with a speed of $\backslash (3,530\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash )$ at $20$ km of altitude $($set in $1976).$

a$.$ Estimate the temperature $($in $\backslash (\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ))$ reached in those flight conditions at the front stagnation point of the airplane. $(1$ point$)$

b$.$ If the pilot needed to decrease that stagnation temperature by $\backslash (180^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ during a mission to avoid damage to the airplane while keeping the same altitude to avoid surface$-$to$-$air missile threats, what would be the maximum flight speed $($in $\backslash (\backslash$mathrm$\{$km$\}/\backslash$mathrm$\{$h$\}\backslash ))$ at which the Blackbird could fly? $(2$ points$)$