$(10$ points$)$ Fig. $2$ shows a concrete dam. Two vertical cross$-$sections are depicted. The face of the dam, its headwater, i$.$e$.$ the reservoir with fresh water, coincides with the xOy in the vertical plane $($shaded in blue$)$ of Fig$\mathrm{.}2$a$.$ The Ox axis coincides with the water level in the dam reservoir. The width of the dam is $120$ m $.$ The depth of water $($counted from an impermeable reservoir bed$)$ is $55$ m $.$ The dam crest is at the same elevation above the bed as the water level in the dam reservoir $($OX axis in Fig$\mathrm{.}2.$ The plane $y=55m$ in Fig. $2$ b is an impermeable dam base.

Fig. $2$

$(3$ points$)$ Calculate the hydrostatic force $F_R$ acting on the dam face.

$(3$ points$)$ Write down three Cartesian coordinates at which $F_R$ is applied.