(1) According to the survey, the gymnasium is 45 degrees west of the north of the school, and the distance from the school to the gymnasium is 2.5 cm.

The actual distance is: 2.5÷150000 =125000 (cm) =1.25 (km).

So the gymnasium is 45 degrees northwest of the school1.25 km;

(2) The distance from the library to the school map is:

1 km = 100000 cm，

100000× 1 50000 =2 (cm),

The location of the library is as follows:

So the answer is: West 45, 1.25.