Exam 1: Units, Trigonometry, and Vectors

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If point A is located at coordinates (-10,7)and point B is located at coordinates (8,-8),what is the distance from A to B if the units of the coordinated system are meters?

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The speed of a boat is often given in knots.If a speed of 5 knots were expressed in the SI system of units,the units would be:

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Vector Vector   Is 2 m long,and vector   Is 5 m long.The length of the sum of the vectors must be ​ Is 2 m long,and vector Vector   Is 2 m long,and vector   Is 5 m long.The length of the sum of the vectors must be ​ Is 5 m long.The length of the sum of the vectors must be ​

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An apartment has 1 100 ft2 of floor space.What is the approximate volume of the apartment?

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A furlong is a distance of 220 yards.A fortnight is a time period of two weeks.A race horse is running at a speed of 6.00 yards per second.What is his speed in furlongs per fortnight?​

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Consider the cosine of any angle between 35° and 40°.If the angle were doubled,what would happen to the cosine of the angle.

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Consider the sine of any angle between 30° and 40°.If the angle were doubled,what would happen to the sine of the angle?

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Which one of the choices below represents the preferred practice regarding significant figures when adding the following: 15.9 + 14 + 77.68 + 6.898?

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A mosquito flies diagonally from a corner at the floor of a rectangular room,with coordinates (0,0,0)to the opposite corner at the ceiling,with coordinates (5.5,3.75,h)m at a rate of 0.8 m/s.If it takes the mosquito 11 seconds to make the direct flight,what is h? ​

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There are other ways of expressing uncertainty besides significant figures.For example,suppose a quantity is known to have a value between 20.4 and 20.0,and our best estimate of the value is midrange at 20.2.We could write the number as 20.2 +/− 0.2 and say that the number has a 1% uncertainty.We would also say it has 3 significant figures.If we square a number with 1% uncertainty and 3 significant figures,what results?

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The mass of a star is 8.0 × 1030 kg,and the mass of a hydrogen atom is 1.67 × 10−27 kg.If we assume that the star is mostly composed of hydrogen,approximately how many atoms are there in the star?

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A student adds two vectors with magnitudes of 200 and 70.Which one of the following is the only possible choice for the magnitude of their sum?

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Vector Vector   Is 3.0 units in length and points along the positive x axis;vector   Is 5.0 units in length and points along a direction 150° from the positive x axis.What is the magnitude of the resulting vector when vectors   And   Are added? Is 3.0 units in length and points along the positive x axis;vector Vector   Is 3.0 units in length and points along the positive x axis;vector   Is 5.0 units in length and points along a direction 150° from the positive x axis.What is the magnitude of the resulting vector when vectors   And   Are added? Is 5.0 units in length and points along a direction 150° from the positive x axis.What is the magnitude of the resulting vector when vectors Vector   Is 3.0 units in length and points along the positive x axis;vector   Is 5.0 units in length and points along a direction 150° from the positive x axis.What is the magnitude of the resulting vector when vectors   And   Are added? And Vector   Is 3.0 units in length and points along the positive x axis;vector   Is 5.0 units in length and points along a direction 150° from the positive x axis.What is the magnitude of the resulting vector when vectors   And   Are added? Are added?

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Modern electroplaters can cover a surface area of 75.0 m2 with one troy ounce of gold (volume = 1.611 cm3).What is the thickness of the electroplated gold?

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The distance to a hypothetical galaxy is estimated at about 7 × 106 light years.A light year is the distance traveled by light in one year;if the speed of light is 3 × 108 m/s,about how far is it from our galaxy to this hypothetical galaxy? (1 year = 3.15 × 107 s)

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A city uses 6.8 × 109 gallons​ of water every day.How many gallons per minute must be pumped from the reservoir to meet the city's water needs?

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A circle has an area of 3.0 m2.A second circle has double the radius of the first.The area of the second circle is ____ times that of the first.

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Which expression is dimensionally consistent with an expression that would yield a value for time−1? (v is velocity,x is distance,and t is time)

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Vector Vector   Points north,and vector   Points east.If   =   −   ,then vector   Points Points north,and vector Vector   Points north,and vector   Points east.If   =   −   ,then vector   Points Points east.If Vector   Points north,and vector   Points east.If   =   −   ,then vector   Points = Vector   Points north,and vector   Points east.If   =   −   ,then vector   Points − Vector   Points north,and vector   Points east.If   =   −   ,then vector   Points ,then vector Vector   Points north,and vector   Points east.If   =   −   ,then vector   Points Points

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Which formula is dimensionally consistent with an expression yielding a value for velocity? (a is acceleration,x is distance,and t is time)

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