If riding a lawnmower engine exerts 19 hp in one minute to move the lawnmower how much work is done

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1

Two rigid transformations are used to map δhjk to δlmn. the first is a translation of vertex h to vertex l. what is the second transformation? a reflection across the line containing hk a rotation about point h a reflection across the line containing hj a rotation about point k

Air is contained in a variable-load piston-cylinder device equipped with a paddle wheel. initially, air is at 400 kpa and 17°c. the paddle wheel is now turned by an external electric motor until 75 kj/kg of work has been transferred to air. during this process, heat is transferred to maintain a constant air temperature while allowing the gas volume to triple. calculate the required amount of heat transfer in kj/kg.