If you walk 1.2 km north and then 1.6 km east, what are the magnitude and direction of your resultant displacement? a. magnitude: 2.00 km; direction: 36.9° east of north b. magnitude: 2.00 km; direction: 53.1° east of north c. magnitude: 1.1 km; direction: 36.9° east of north d. magnitude: 1.1 km; direction: 53.1° east of north

When fat comes in contact with sodium hydroxide, it produces soap and glycerin. determine whether this is a physical change or a chemical change. explain your answer

What is the fate of the electrons that interact with a specimen in an electron microscope?

Aparticle of mass m is projected with an initial velocity v0 in a direction making an angle α with the horizontal level ground as shown in the figure. the motion of the particle occurs under a uniform gravitational field g pointing downward. (a) write down the lagrangian of the system by using the cartesian coordinates (x, y). (b) is there any cyclic coordinate(s). if so, interpret it (them) physically. (c) find the euler-lagrange equations. find at least one constant of motion. (d) solve the differential equation in part (c) and obtain x and y coordinates of the projectile as a function of time. (e) construct the hamiltonian of the system, h, and write down the hamilton’s equations (canonical equations) of motion.