Abeachgoer leaves a pair of sandals on the shore while she swims. when she puts the sandals on again, the bottom of her feet will feel hot because

conduction of heat.

The radiation of Sun warmed the sole of the sandals overtime. The heat from the sole transferred via conduction to the her feet. Conduction is the mode of heat transfer when two objects are in contact and have temperature difference. Hence, her feet feels hot after putting on the sandals again as heat from the sole conducted to her feet.  

one person pulls 90n one way and the other has 100n pulling the other way.

so the net force = 90 - 100 = -10n,

or the ans can be 10n if the picture shows -90n and 100n instead.