Problem 1: Convert $135^\circ$ to radians.

Problem 2: Convert $\frac{5\pi}{3}$ radians to degrees.

Problem 3: Find the reference angle for $\theta = 240^\circ$.

Problem 4: Find a positive angle less than $360^\circ$ that is coterminal with $-400^\circ$.

Problem 5: A circle has a radius of 15 cm. Find the length of the arc intercepted by a central angle of $150^\circ$.

Problem 6: A wind turbine blade is 30 meters long and rotates at 15 revolutions per minute (rpm). Find the linear speed of the tip of the blade in meters per second.

Problem 7: A water pipe has an internal radius of 20 cm. If it is partially filled with water subtending an angle of $\frac{2\pi}{3}$ at the center, what is the cross-sectional area of the water?