Part A What is the angle 0 between vectors A and B if A = 7 î – 2 j and B=-3 î +5 ĵ? Express your answer as an integer and include the appropriate units. HA ? Value Units Submit Request Answer Part B What is the angle 0 between vectors A and B if A = 3 î +2 ĵ and B= 4 î – 6 ĝ? Express your answer as an integer and include the appropriate units. HẢ ? Value Units Submit Request Answer

Over the Christmas break, you are making some extra money for buying presents by working in a factory, helping to move crates around. At one particular time, you find that all the handtrucks, dollies, and carts are in use, so you must move a crate across the room a straight-line distance of 35.0 m without the assistance of these devices. You notice that the crate has a rope attached to the middle of one of its vertical faces. You decide to move the crate by pulling on the rope. The crate has a mass of 130 kg, and the coefficient of kinetic friction between the crate and the concrete floor is 0.350. (a) Determine the angle relative to the horizontal at which you should pull upward on the rope so that you can move the crate over the desired distance with the force of the smallest magnitude. (b) At this angle of pulling on the rope, how much work do you do in dragging the crate over the desired distanced?

You operate a restaurant that has many large, circular tables. At the center of each table is a Lazy Susan that can turn to deliver salt, pepper, jam, hot sauce, bread, and other items to diners on the other side of the table. A fancy flower arrangement is located at the center of each Lazy Susan, and the turning of the flower arrangement is beautiful to you. Because of your interest in model trains, you decide to replace each Lazy Susan with a circular track on the table around which a model train will run. You can load the various condiments in the cars of the train and press a button to operate the train, causing the train to begin moving around the circle and deliver the load to your fellow diners! The train is of mass 1.96 kg and moves at a speed of 0.18 m/s relative to the track. After a few days, you realize that you miss the beautiful turning flower arrangements. So you come up with a new scheme. You return the Lazy Susan to the table and mount the circular track on the platform of the Lazy Susan, which has a friction-free axle at its center. The radius of the circular track is 40.0 cm (measured halfway between the rails) and the platform of the Lazy Susan is a uniform disk of mass 3.00 kg and radius 48.0 cm. You finally equip all of your tables with the new apparatus and open your restaurant. As a demonstration to the diners, you mount one salt shaker and one pepper shaker, having a mass of 0.100 kg each, onto a flatcar and push the button to deliver the condiments to the other side of the table! How long does it take to deliver the condiments to the exact opposite side of the table? Ignore the moment of inertia of the flower arrangement, since its mass is all close to the rotation axis.

Let the four compass directions north, east, south, and west be represented by unit vectors ne . . and respectively. Vertically up and down are represented as u and d. Let us also identify unit vectors that are halfway between these directions such as for northeast. Rank the magnitudes of the following cross products from largest to smallest. If any are equal in magnitude or are equal to zero, show that in your ranking, (a) (b) (c) (d) (e)