Two vectors, A and B, have magnitudes of 10 and 15. The cross product of these vectors has magnitude 32. What is the angle between vectors A and B?

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.

Two 2.0-cm-diameter disks face each other, 1.0 mm apart. they are charged to ±10 nc. what is the electric field strength between the disks? a proton is shot from the negative disk toward the positive disk. what launch speed must the proton have to just barely reach the positive disk?

Aswimming pool whose volume is 10 comma 000 gal contains water that is 0.01% chlorine. starting at tequals0, city water containing 0.003% chlorine is pumped into the pool at a rate of 5 gal/min. the pool water flows out at the same rate. what is the percentage of chlorine in the pool after 1 hour? when will the pool water be 0.006% chlorine?