The atmospheric pressure above a swimming pool changes from 753 to 772 mm of mercury. the bottom of the pool is a rectangle (11 m cross product 21 m). by how much does the force on the bottom of the pool increase

Change in pressure : 772-753 = 19 mm Hg 
Since 1 mm Hg = 133 Pa Hg
 Then, 19 mm Hg = 2527 Pa Hg
 Area of rectangular pool = L* B = 11 x 21 = 231 m^2
 To find the force, we multiply the area by the change in pressure: 2527 (231) = 583737N

Since we are talking about the pressure of water at a certain height, we can associate hydrostatic pressure or hydrostatic force. The formula relating this two is:

P = F/A
So,
F = P*A

To find the change of force, simply multiply the change in pressure to the cross-sectional area of the swimming pool. To report in terms of Newtons, let's convert mmHg to Pa (760 mmHg = 101325 Pa).

F = (772 - 753 mmHg)(101325 Pa/760 mmHg)(11 m × 21 m)
F = 585,151.875 N