 8.2.8.1.90: Cubic meters, m3, are a measure of .
 8.2.8.1.91: Millimeters, mm, are a measure of .
 8.2.8.1.92: Hectares, ha, are a measure of .
 8.2.8.1.93: Centimeters, cm, are a measure of .
 8.2.8.1.94: Meters, m, are a measure of .
 8.2.8.1.95: Liters, /, are a measure of .
 8.2.8.1.96: Kiloliters, k/, are a measure of .
 8.2.8.1.97: Square meters, m2, are a measure of .
 8.2.8.1.98: Cubic centimeters, cm3, are a measure of .
 8.2.8.1.99: Kilometers, km, are a measure of .
 8.2.8.1.100: Centiliters, c/, are a measure of .
 8.2.8.1.101: Cubic kilometers, km3, are a measure of .
 8.2.8.1.102: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.103: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.104: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.105: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.106: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.107: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.108: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.109: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.110: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.111: In Exercises 1322, indicate the metric unit of measurement that you...
 8.2.8.1.112: The length of a football field, including both end zones, is about ...
 8.2.8.1.113: A U.S. postage stamp is about how wide and how long? a) 2 cm * 3 cm...
 8.2.8.1.114: The distance between Los Angeles and San Diego could be how far? a)...
 8.2.8.1.115: The longest snake, a fullgrown reticulated python, may be about ho...
 8.2.8.1.116: A ruler is about how wide? a) 4 mm b) 4 cm c) 4 dm
 8.2.8.1.117: The diameter of a coffee cup is about which of the following? a) 8 ...
 8.2.8.1.118: The worlds tallest building, Burj Khalifa, in Dubai is about how ta...
 8.2.8.1.119: The length of the New River Gorge Bridge near Fayetteville, West Vi...
 8.2.8.1.120: In Exercises 3136, (a) estimate the item in metric units and (b) me...
 8.2.8.1.121: In Exercises 3136, (a) estimate the item in metric units and (b) me...
 8.2.8.1.122: In Exercises 3136, (a) estimate the item in metric units and (b) me...
 8.2.8.1.123: In Exercises 3136, (a) estimate the item in metric units and (b) me...
 8.2.8.1.124: In Exercises 3136, (a) estimate the item in metric units and (b) me...
 8.2.8.1.125: In Exercises 3136, (a) estimate the item in metric units and (b) me...
 8.2.8.1.126: In Exercises 37 44, indicate the metric unit of measurement you wou...
 8.2.8.1.127: In Exercises 37 44, indicate the metric unit of measurement you wou...
 8.2.8.1.128: In Exercises 37 44, indicate the metric unit of measurement you wou...
 8.2.8.1.129: In Exercises 37 44, indicate the metric unit of measurement you wou...
 8.2.8.1.130: In Exercises 37 44, indicate the metric unit of measurement you wou...
 8.2.8.1.131: In Exercises 37 44, indicate the metric unit of measurement you wou...
 8.2.8.1.132: In Exercises 37 44, indicate the metric unit of measurement you wou...
 8.2.8.1.133: In Exercises 37 44, indicate the metric unit of measurement you wou...
 8.2.8.1.134: A credit card has an area of about a) 50 cm2 . b) 50 mm2 . c) 50 dm2 .
 8.2.8.1.135: The area of a city lot is about a) 800 m2 . b) 800 hm2 . c) 800 cm2 .
 8.2.8.1.136: The area of a city lot is about a) 1 8 m2 . b) 1 8 ha. c) 1 8 km2 .
 8.2.8.1.137: The area of a floor tile is about a) 930 m2 . b) 930 km2 . c) 930 cm2
 8.2.8.1.138: The area of one side of a nickle is about a) 3 cm2 . b) 3 m2 . c) 3...
 8.2.8.1.139: The area of the screen of a tabletop TV is about a) 1200 dm2 . b) 1...
 8.2.8.1.140: The area of Grand Canyon National Park is about a) 4900 m2. b) 4900...
 8.2.8.1.141: The area of a U.S. flag is about a) 2.2 cm2 . b) 2.2 m2 . c) 2.2 km2 .
 8.2.8.1.142: In Exercises 5358, (a) estimate the area of the item in metric unit...
 8.2.8.1.143: In Exercises 5358, (a) estimate the area of the item in metric unit...
 8.2.8.1.144: In Exercises 5358, (a) estimate the area of the item in metric unit...
 8.2.8.1.145: In Exercises 5358, (a) estimate the area of the item in metric unit...
 8.2.8.1.146: In Exercises 5358, (a) estimate the area of the item in metric unit...
 8.2.8.1.147: In Exercises 5358, (a) estimate the area of the item in metric unit...
 8.2.8.1.148: In Exercises 59 66, determine the metric unit that would best be us...
 8.2.8.1.149: In Exercises 59 66, determine the metric unit that would best be us...
 8.2.8.1.150: In Exercises 59 66, determine the metric unit that would best be us...
 8.2.8.1.151: In Exercises 59 66, determine the metric unit that would best be us...
 8.2.8.1.152: In Exercises 59 66, determine the metric unit that would best be us...
 8.2.8.1.153: In Exercises 59 66, determine the metric unit that would best be us...
 8.2.8.1.154: In Exercises 59 66, determine the metric unit that would best be us...
 8.2.8.1.155: In Exercises 59 66, determine the metric unit that would best be us...
 8.2.8.1.156: A shoe box a) 7780 mm3 b) 7780 dm3 c) 7780 cm3
 8.2.8.1.157: Water that could fit in a thimble a) 3 m/ b) 3 / c) 3 d/
 8.2.8.1.158: Water in a 24ftdiameter aboveground circular swimming pool a) 55...
 8.2.8.1.159: Soda in a can of soda a) 355 / b) 355 m/ c) 355 m3
 8.2.8.1.160: A carryon suitcase a) 0.04 cm3 b) 0.04 mm3 c) 0.04 m3
 8.2.8.1.161: Juice that can be squeezed out of an orange a) 120 k/ b) 120 m/ c) ...
 8.2.8.1.162: Air in a soccer ball a) 5000 m3 b) 5000 cm3 c) 5000 mm3
 8.2.8.1.163: Air in a balloon with a diameter of about 17 meters a) 2600 m3 b) 2...
 8.2.8.1.164: In Exercises 7578, (a) estimate the volume in metric units and (b) ...
 8.2.8.1.165: In Exercises 7578, (a) estimate the volume in metric units and (b) ...
 8.2.8.1.166: In Exercises 7578, (a) estimate the volume in metric units and (b) ...
 8.2.8.1.167: In Exercises 7578, (a) estimate the volume in metric units and (b) ...
 8.2.8.1.168: One liter of liquid has the equivalent volume of which of the follo...
 8.2.8.1.169: One cubic meter has the equivalent volume of which of the following...
 8.2.8.1.170: One milliliter of liquid has the equivalent volume of which of the ...
 8.2.8.1.171: A hectare has an area of about how many acres: 2.5, 25, or 250?
 8.2.8.1.172: Area Use a metric ruler to measure the length and width of the side...
 8.2.8.1.173: Area Use a metric ruler to find the radius of the circle. Then comp...
 8.2.8.1.174: MerryGoRound The base of the merrygoround (or carousel) at Hers...
 8.2.8.1.175: Painting The total area of a framed painting including the matting ...
 8.2.8.1.176: A Walkway A rectangular building 50 m by 70 m is surrounded by a wa...
 8.2.8.1.177: Farmland Kim Martello has purchased a farm that is in the shape of ...
 8.2.8.1.178: Childrens Playground The dimensions of a large rectangular playgrou...
 8.2.8.1.179: Volume of Water a) What is the volume of water in a rectangular swi...
 8.2.8.1.180: Cost of Paint The first coat of paint for the outside of a building...
 8.2.8.1.181: Volume of a saucepan A saucepan has a diameter of 18.0 cm and a hei...
 8.2.8.1.182: Fish Tank Volume A rectangular fish tank is 70 cm long, 40 cm wide,...
 8.2.8.1.183: HotWater Heater A cylindrical shaped hotwater heater has a diamet...
 8.2.8.1.184: How many times larger is a square kilometer than a square hectometer?
 8.2.8.1.185: How many times larger is a square kilometer than a square dekameter?
 8.2.8.1.186: How many times larger is a cubic meter than a cubic decimeter?
 8.2.8.1.187: How many times larger is a cubic centimeter than a cubic millimeter?
 8.2.8.1.188: In Exercises 99104, replace the question mark with the appropriate ...
 8.2.8.1.189: In Exercises 99104, replace the question mark with the appropriate ...
 8.2.8.1.190: In Exercises 99104, replace the question mark with the appropriate ...
 8.2.8.1.191: In Exercises 99104, replace the question mark with the appropriate ...
 8.2.8.1.192: In Exercises 99104, replace the question mark with the appropriate ...
 8.2.8.1.193: In Exercises 99104, replace the question mark with the appropriate ...
 8.2.8.1.194: In Exercises 105108, fill in the blank.419 cm3 = m/
 8.2.8.1.195: In Exercises 105108, fill in the blank.435 cm3 = /
 8.2.8.1.196: In Exercises 105108, fill in the blank.76 k/ = m3
 8.2.8.1.197: In Exercises 105108, fill in the blank.4.2 / = cm3
 8.2.8.1.198: Glacier In Exercises 109110, assume that a part of a rectangular gl...
 8.2.8.1.199: Glacier In Exercises 109110, assume that a part of a rectangular gl...
 8.2.8.1.200: In Exercises 111 and 112, fill in the blank to make a true statemen...
 8.2.8.1.201: In Exercises 111 and 112, fill in the blank to make a true statemen...
 8.2.8.1.202: Conversions In Example 3, we illustrated how to change an area in a...
 8.2.8.1.203: Water Usage a) How much water do we use daily? On the average, peop...
 8.2.8.1.204: The Meter The definition of the meter has changed several times thr...
Solutions for Chapter 8.2: The Metric System
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 8.2: The Metric System
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Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.