An annular ring with a uniform surface charge density σ sits in the xy plane, with its center at the origin of the coordinate axes. The annulus has an inner radius r1 and outer radius r2. Required:
If you can find symmetries in a physical situation, you can often greatly simplify your calculations. Find a symmetry in the annular ring before calculating the potential along the z axis through the ring's center.

Astronomers discover an exoplanet (a planet of a star other than the sun) that has an orbital period of 3.87 earth years in its circular orbit around its sun, which is a star with a measured mass of 3.59 x 1030 kg. find the radius of the exoplanet's orbit.

The magnitude of the amount of energy released by burning a fuel source, measured in energy per unit mass, is called its fuel value. note that the fuel value is the negative of the isobaric specific heat of combustion for the fuel. if all the energy obtained from burning 1.23 pounds of butane with a fuel value of 10.85 kcal/g is used to heat 128.0 kg of water at an initial temperature of 18.3 °c, what is the final temperature? note that 1 lb = 453.6 g.

Anoche fuimos al restaurante el gusto. jaime le (1) (pedir) al camarero una mesa en la sección de no fumar. yo (2) (pedir) chuleta de cerdo con champiñones, papas y ensalada y jaime (3) (pedir) mariscos, arroz y ensalada. el restaurante estaba lleno (full) por eso no nos (4) (servir) muy rápido (very fast), pero la comida estaba deliciosa. no me lo vas a creer (you won't believe it) pero ¡jaime (5) (repetir) arroz y mariscos! ¡dos porciones (orders)! ¿ya entiendes por qué él no (6) (dormir) bien anoche?