The electromagnetic field is invariant under a gauge transformation of the scalar and vector potential given by a rightarrow a + psi (r, t), phi rightarrow phi - l / c psi / t, where psi is arbitrary (but differentiable). what effect does this gauge transformation have on the lagrangian of a particle moving in the electromagnetic field? is the motion affected?

Aregular polygon has angkes of size 150° each. how many side has the polygon

Asubject in a clinical research trial experiences a serious, unanticipated adverse drug experience. how should the investigator proceed, with respect to the irb, after the discovery of the adverse event occurrence? a. do not report the adverse drug experience to the irb since it is a common adverse experience. b. report the adverse drug experience to the irb only if there are several other occurrences. c. report the adverse drug experience as part of the continuing review report. d. report the adverse drug experience in a timely manner, in keeping with the irb's policies and procedures, using the forms or the mechanism provided by the irb.

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.