Which of the following do not require a medium for transmission?

If $\vec{E}$ and $\vec{K}$ represent the electric field and propagation vectors of electromagnetic $(EM)$ waves in a vacuum,respectively,then the magnetic field vector $\vec{B}$ is given by: (where $\omega$ is the angular frequency).

Given below are two statements:
Statement $I$: $A$ time-varying electric field is a source of a changing magnetic field and vice-versa. Thus,a disturbance in an electric or magnetic field creates $EM$ waves.
Statement $II$: In a material medium,the $EM$ wave travels with speed $v = \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$.
In the light of the above statements,choose the correct answer from the options given below:

The following travelling electromagnetic wave $E_x=0$,$E_y=E_0 \sin (kx + \omega t)$,$E_z=-2E_0 \sin (kx - \omega t)$ is:

An electromagnetic wave of frequency $3 \, GHz$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium will be $....... \times 10^{-2} \, cm$.

$A$ plane $EM$ wave travelling along $z-$ direction is described by $\vec E = E_0 \sin(kz - \omega t)\hat i$ and $\vec B = B_0 \sin(kz - \omega t)\hat j$. Show that:
$(i)$ The average energy density of the wave is given by $U_{av} = \frac{1}{4} \epsilon_0 E_0^2 + \frac{1}{4} \frac{B_0^2}{\mu_0}$.
$(ii)$ The time-averaged intensity of the wave is given by $I_{av} = \frac{1}{2} c \epsilon_0 E_0^2$.