Afan is turned off, and its angular speed decreases from 10.0 rad/s to 6.3 rad/s in 5.0 s. what is the magnitude of the angular acceleration of the fan?

Angular acceleration can be defined as the change in the angular velocity over time.
Angular acceleration can be calculated using the following rule:
Angular acceleration = change in angular velocity / time
where:
change in angular acceleration = 6.3 - 10 = -3.7 rad/sec
time = 5 sec

Substitute in the above equation to get the angular acceleration as follows:
angular acceleration = (-3.7) / 5 = -0.74 rad/sec^2

Note that the negative sign is only an indication that the the speed is decreasing (deceleration)
Since the question is only asking for the magnitude, therefore, the answer would simply be 0.74 rad/sec^2

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.