Find a sequence of type II row operations (adding one row to another) which result in replacing Ri with Rj and Rj with Ri for any rows i and j of a matrix M. Hence, show that every type I operation (swapping two rows) can be obtained as a sequence of operations of types II and III.

Mass (kg) force (n) 5 25 10 50 15 75 20 100 a student was trying to find the relationship between mass and force. he placed four different masses on a table and pulled them using a spring scale. the table shows the different masses used in the experiment and the force required to pull each mass. the student concluded that more force was required to pull heavier objects. what comment would you make regarding his conclusion? a) no clear relation can be observed between mass and force from the data. b) there is a direct proportion between the mass and force listed in the table. c) gravity should have been taken into account while performing the experiment. d) there is an inverse proportion between the mass and force listed in the table.

Wave functions describe orbitals in a hydrogen atom. each function is characterized by 3 quantum numbers: n, l, and ml. if the value of n = 2: the quantum number l can have values from to . the total number of orbitals possible at the n = 2 energy level is .

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.