The triangular sign in Figure $1$ is embeddee in a concrete block at B $.$ The air pressure $($called stagnation pressure$)$ againsrt the vertical surface for a given wind speed is P$0$ abd uniform on the triangular surface $.1-$ Determine the sum of the pressure force wrench $($vector$)$ acting on the triangular surface in terms of $P_0$ and $L$

$2-$a$)$ Prove that the moment about $O$ of the pressure force wrench is of the form

$M(O)={\left[\begin{array}{c}x\\ 0\\ Z\end{array}\right]}_{(x,y,z)}$

Determine $x$ and $Z$ in terms of $P_0$ and $L$

$3-$ Prove that the pressure force wrench can be reduced to a unique sliding vector.

$4-$ Prove that the line of action of the equivalent force passes through the point of coordinates $O{I}^{**}={\left[\begin{array}{c}-a\\ 0\\ -a\end{array}\right]}_{(x,y,z)}$ and give the value of $a$ in terms of $L.$ What is this particular point $I**?$

$5-$ Using the shifting equation, give the moment about $B$ of the force wrench associated with the air pressure in terms of $x,Z,P_0,L$ and $d.$ Same question but give the moment about $B$ in terms of $P_0,L,$a and $d.$

$7-$ Numerical application: find the sum and moment at $B$ for $L=2m$;$d=1m$;$P_0=1\mathrm{.}4$kPa $($corresponding to a wind speed of $100k\frac{m}{h})$