You have a sample of gas at -30 C. You wish to increase the rms speed by 12%. To what temperature should the gas be heated?

Answer 1

rms means the square root of the mean squared.

So increasing rms by 1.12 means increasing energy by 1.12 squared, or 1.25
But temp is a measure of avg KE, or avg v^2, so temp should increase by 1.25
The original temp was 273-30K, or 243, so the new tempwill be 305K.