Electric field lines can never cross. Woodward crossed electric field lines indicate?

An ice-making machine inside a refrigerator operates in a carnot cycle. it takes heat from liquid water at 0.0 degrees celsius and rejects heat to a room at a temperature of 19.2 degrees celsius. suppose that liquid water with a mass of 76.3kg at 0.0 degrees celsius is converted to ice at the same temperature. take the heat of fusion for water to be l_f = 3.34*10^5 j/kg. how much energy e must be supplied to the device? express your answer in joules.

Does heating a metal wire increase or decrease its electrical resistance? why?

Using a caesar cypher with an offset of three characters (a -> d, b -> e, z -> c), what would be the correct cypher text for the plain text "attack at dawn"?