An electromagnetic wave of wavelength 435 nm is traveling in vacuum in the —z direction. The electric field has an amplitude of 2.70 x 10^-3 V/m and is parallel to the x axis. What are the frequency and the magnetic-field amplitude of this wave? In calculating the amplitude of the magnetic field, you divide the electric-field amplitude by the speed of light, which requires you to convert some units. Which of the following is equivalent to 1 T? a. 1 (N/A. m)
b. 1 (N/c. m)
c. 1 (N. s/C. m)
d. 1 (V. s/m^2)

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.

Argon is adiabatically compressed from an initial volume of 16 liters to a final volume of 2 liters. by what factor do the following quantities change? do they increase or decrease? (a) the rms speed (b) the thermal energy of the gas (c) the molar specific heat cv (d) the pressure

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)