1) a) Find a plane model for the connected sum of two tori: T#T = 2 T. b) Draw an arbitrary closed curve on the torus that does not bound a disk on the torus. Depict this curve on the plane model of the torus.
c) Draw a correspondent closed curve on 2 T. Depict this curve on the plane model of 2 T.
2) Does the surface n T have the fixed point property?

In the first law of thermodynamics, triangle e=q-w, what does q stand for

Avolcano erupts next to a grassland area in a valley. a. describe three ways in which material released by the volcano could impact the grassland area. b. describe three ways in which the grassland ecosystem could recover after a volcanic eruption.

Asled is being held at rest on a slope that makes an angle θ with the horizontal. after the sled is released, it slidesa distance d1 down the slope and then covers the distance d2 alongthe horizontal terrain before stopping. find the coefficient ofkinetic friction μk between the sled and the ground, assumingthat it is constant throughout the trip. find the coefficient of kinetic frictionμk. express your answer in terms of someor all of the variables d1, d2, and θ.