The question in the image asks to convert the vector $(3, 4)$ from Cartesian (rectangular) coordinates to polar form. Here's how to solve it step-by-step:

1. Magnitude (r): The magnitude of the vector is calculated using the Pythagorean theorem: $r = \sqrt{x^2 + y^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$

2. Angle (θ): The angle θ is found using the inverse tangent function: $\theta = \tan^{-1}\left(\frac{y}{x}\right) = \tan^{-1}\left(\frac{4}{3}\right) \approx 53.13^\circ$

So, the polar form of the vector $(3, 4)$ is: $(5, 53.13^\circ)$

Answer: The correct option is (5, 53.13°).

For Question 9, it asks for the period of a sinusoidal wave with a frequency of 2 Hz. The period $T$ of a wave is the reciprocal of its frequency $f$: $T = \frac{1}{f}$ Given $f = 2 \, \text{Hz}$, the period is: $T = \frac{1}{2} = 0.5 \, \text{seconds}$

Let me know if you'd like any additional explanations or details!

Here are 5 related questions for further practice:

1. How do you convert a polar vector back to Cartesian coordinates?
2. What is the polar form of the vector $(-3, 4)$?
3. How would the vector $(3, 4)$ look if rotated 45 degrees counterclockwise?
4. What is the frequency of a wave with a period of 0.25 seconds?
5. How does changing the frequency of a wave affect its wavelength?

Tip: When converting vectors, always remember to check if the angle is in the correct quadrant based on the signs of $x$ and $y$.