A rectangular gate $5$ m wide and $9$ m high is hinged at the top in a vertical dam. The gate holds $10$ m of oil $($s$.$g$.=0\mathrm{.}84)$ whose surface is held under vacuum at $-16\mathrm{.}48$ kPa. $($a$)$ Determine the magnitude of the hydrostatic force acting on the gate. $($b$)$ Determine the location of the resultant force on the gate. $($c$)$ Determine the horizontal force required on the left side of the gate applied at the bottom required to open the gate.