The first thing you want to do is find your knowns and unknowns.
The initial angular velocity is 3550 rev/min and the final is 0 (because the centrifuge will be at rest).
We also have the change in theta which is 48.0 revs.
In order to get it in the right units, you are going to want to convert everything from revs to rads and mins to secs.
So, 3550 rev/min x (2π rads/1 rev) x (1 min/60 secs) = 372.28 rads/sec
And 48.0 revs x (2π rad/1 rev) = 301.59 rads
From here, you can use one of the problems you've learned in physics before to find velocity, distance, acceleration, time and so forth. With this problem you are going to want to use the
v^2 = v0^2 + 2a (x-xo) but for angular velocity you'll use the omega, alpha, and theta symbols (same thing however)
So, when you plug everything in you get :
0 = (372.28 rads/sec)^2 +2a (301.59 rads)
And solve for a. Hope that helps!