Afast-moving superhero in a comic book runs around a circular, 70-m-diameter track five and a half times (ending up directly opposite her starting point) in 3.0s, what is her angular speed, in rad/s?

People with normal vision cannot focus their eyes underwater if they aren't wearing a face mask or goggles and there is water in contact with their eyes. in a simplified model of the human eye, the aqueous and vitreous humors and the lens all have a refractive index of 1.40, and all the refraction occurs at the cornea, whose vertex is 2.60 cm from the retina. with the simplified model of the eye, what corrective lens (specified by focal length as measured in air) would be needed to enable a person underwater to focus an infinitely distant object? (be careful-the focal length of a lens underwater is not the same as in air! assume that the corrective lens has a refractive index of 1.62 and that the lens is used in eyeglasses, not goggles, so there is water on both sides of the lens. assume that the eyeglasses are 2.05cm in front of the eye.)

Find an expression for the electric field e⃗ at the center of the semicircle. hint: a small piece of arc length δs spans a small angle δθ=δs /r, where r is the radius. express your answer in terms of the variables q, l, unit vectors i^, j^, and appropriate constants.

If you drive 12 miles north and 35 miles east, what is the direct distance between you and your starting point?