PHYSICAL SCIENCE
Summarize Newton's first law of motion by telling how an object in motion's inertia is changed and how an object at rest is affected.
PROBABILITY
Deal with combining rigid motions. Given two rigid motions M and N, we can combine the two rigid motions by first applying it and then applying X to the result. The rigid motion defined by combining M and N (M goes first, N goes second) is called the product of M and N. In each case, state whether the rigid motion M is proper or improper. (a) M is the product of a proper rigid motion and an improper rigid motion. (b) M is the product of an improper rigid motion and an improper rigid motion. (c) M is the product of a reflection and a rotation. (d) M is the product of two reflections.
LINEAR ALGEBRA
Prove that the composition of two rigid motions on $R^n$ is a rigid motion.
LINEAR ALGEBRA
Let $V$ be a real inner product space. $\\$ (a) Prove that any translation on$V$is a rigid motion.$ $ (b) Prove that the composite of any two rigid motions on V is a rigid motion on V.
PRECALCULUS
For the chocolate stirrer, the situation with the wheel and stirrer blade represents a conversion between linear motion and circular motion. a. Do both motions represent constant velocity? Explain. b. Do both the wheel and the blade represent motions in a constant direction? Explain.
PHYSICS
The wheels on a moving bicycle have both translational (or linear) and rotational motions. What is meant by the phrase "a rigid body, such as a bicycle wheel, is in equilibrium"? (a) The body cannot have translational or rotational motion of any kind. (b) The body can have translational motion, but it cannot have rotational motion. (c) The body cannot have translational motion, but it can have rotational motion. (d) The body can have translational and rotational motions, as long as its translational acceleration and angular acceleration are zero.
EARTH SCIENCE
a. What are the two major motions of Earth as it travels through space? b. Which motion causes day and night?
LINEAR ALGEBRA
Determine whether the statement is true or false. The composition of two rigid motions on $R^n$ is a rigid motion on $R^n$.
PHYSICAL SCIENCE
a. Identifying What are the two major motions of Earth as it travels through space? b. Explaining Which motion causes day and night?
PREALGEBRA
Slides, flips, and turns are called rigid motions of the plane. Based on the Investigations, describe two characteristics of a rigid motion of the plane.
GEOMETRY
Complete the sentence. Two geometric figures are _ if and only if there is a rigid motion or a composition of rigid motions that moves one of the figures onto the other.
PROBABILITY
Deal with combining rigid motions. Given two rigid motions M and N, we can combine the two rigid motions by first applying it and then applying X to the result. The rigid motion defined by combining M and N (M goes first, N goes second) is called the product of M and N. Suppose that a rigid motion it is the product of a reflection with axis $$ l_1 $$ and a reflection with axis $$ l_2 $$ , where $$ l_1 $$ and $$ l_2 $$ intersect at a point C. Explain why M must be a rotation with center C.
PHYSICS
You have a pendulum pulled to the side, a heavy beach ball pushed partly under water, and a medicine ball lifted some height above the ground. Each object is then released. (a) Draw a picture of the motion of each object and a motion diagram for each. (b) Indicate the equilibrium position. (c) Draw two or more force diagrams at key points in the motion. (d) Use (a) through (c) to reason whether the motions of these objects can be considered vibrational motions.
GEOMETRY
Describe how you can find a rigid motion or composition of rigid motions to map a segment to a congruent segment and an angle to a congruent angle.
PHYSICAL SCIENCE
For one day, write down a brief description of the different kinds of motions you see. Work with a group to generate a common list of the different kinds of motions observed. What reference points did you use to detect the motion? How did these reference points help you determine motion? Compare your list with those from other groups in your class.
HEALTH
Do a time-and-motion study for a common kitchen task, such as making a salad or washing dishes. Count the motions, such as the number of trips to the refrigerator, and time the entire task. Summarize and evaluate your findings in a report. How could you use less time and fewer motions?
PROBABILITY
At a homeowners' association meeting, a board member can vote yes, vote no, or abstain on a motion. There are three motions on which a board member must vote. (a) Determine the number of sample points in the sample space. (b) Construct a tree diagram and determine the sample space. If all votes are equally likely, determine the probability that a board member votes (c) No, yes, no in that order. (d) Yes on exactly two of the motions. (e) Yes on at least one motion.
PHYSICAL SCIENCE
Write a short essay in which you create an analogy to describe particle motion. Compare the movements and positions of people dancing with the motions of water molecules in liquid water and in water. vapor.
PHYSICAL SCIENCE
The motion of molecules that most affects temperature is (a) translational motion. (b) rotational motion. (c) internal vibrational motion. (d) simple harmonic motion.
GEOMETRY
Choose the correct term to complete each sentence. • composition of rigid motions • glide reflection • image • line of reflection • line of symmetry • preimage • rigid motion • rotation • translation. The result of a transformation is called the _____.
EARTH SCIENCE
Scientists look for patterns to understand the natural world. Give three examples of patterns that can be used to understand plates and plate motions. Briefly describe how each is related to plates and plate motion.
QUESTION
A music department consists of a band director and a music teacher. Decisions on motions are made by voting. If both members vote in favor of a motion, it passes. If both members vote against a motion, it fails. In the event of a tie vote, the principal of the school votes to break the tie. For this voting scheme, determine the Banzhaf power index for each department member and for the principal.
PHYSICS
You are an observer on the ground. (a) Draw two motion diagrams representing the motions of two runners moving at the same constant speeds in opposite directions toward you.Runner 1, coming from the east, reaches you in 5 s, and runner 2 reaches you in 3 s. (b) Draw a motion of diagram for the second runner as seen by the first runner.
PHYSICS
The earth’s magnetic field strength is $5.0 \times 10^{-5} \mathrm{T}$. How fast would you have to drive your car to create a 1.0 V motional emf along your 1.0-m-tall radio antenna? Assume that the motion of the antenna is perpendicular to $\vec{B}$.
GEOMETRY
Choose the correct term to complete each sentence. • composition of rigid motions • glide reflection • image • line of reflection • line of symmetry • preimage • rigid motion • rotation • translation. The composition of a reflection and a translation is called a(n) _____.