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Page "Cartesian coordinate system" ¶ 85
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where and are
`` Clay '', he said, `` where are we goin ''??
`` Stay right here where you are, kid '', he called.
I asked the same questions inside the launch-control rooms of an Atlas missile base in Wyoming, where officers who wear sidearms are manning the `` commit buttons '' that could start a war -- accidentally or by design -- and in the command centers where other pistol-packing men could give orders to push such buttons.
they are the places where Persians live.
In Persia, where practically speaking there are no museums or libraries or, for that matter, hardly any books, the twins run free.
Even in domains where detailed and predictive understanding is still lacking, but where some explanations are possible, as with lightning and weather and earthquakes, the appropriate kind of human action has been more adequately indicated.
Not discussed here are some military problems of modern times such as undersea warfare, where the surveillance, sending, transmitting, and receiving are all so inadequate that networks and decision making are not the bottlenecks.
Ideally speaking, it should be allowed to operate only where the public has a great stake in the continuity of supply or services, and where the actions of a single proprietor are secondary to the needs of society.
Examples are in public utilities, making military aircraft and accessories, or where the investment and risk for a proprietorship would be too great for a much needed project impossible to achieve by any means other than the corporate form, e.g. constructing major airports or dams.
Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.
`` On each side of the Hoogli, where we are now sailing, are the Hindoo cottages, as thick together as the houses in our seaports.
but it is perennially restructured in situations where anchors are dragged or lost.
In this essay, we are, along with most historians, interested in the more general or more inclusive ideas, that are so to speak `` writ large '' in history of literature where they recur continually.
The novel, which is not merely dystopian but also brilliantly satiric, describes a future America where one-sixteenth of the population, the men who run advertising agencies and big corporations, control the rest of the people, the submerged fifteen-sixteenths who are the workers and consumers, with the government being no more than `` a clearing house for pressures ''.
Around that statue in the green park where children play and lovers walk in twos and there is a glowing view of the whole city, in that park are the rows of marble busts of Garibaldi's fallen men, the ones who one day rushed out of the Porta San Pancrazio and, under fire all the way, up the long, straight narrow lane to take, then lose the high ground of the Villa Doria Pamphili.
For instance, so-called `` conservative '' organizations, some of them secret, are sprouting in the garden of joining where `` liberal '' organizations once took root.
They enlisted the help of the New Jersey congressman, who has been able to trace the letters to the national archives, where they are available on microfilm.
The speed is controlled by pressing on the two brake buttons located where the index finger and thumb are placed when holding the motor.

where and unit
where is the body force per unit mass, is the pressure, and is the deviatoric stress.
Differences include where the logistic service transfers artillery ammunition to artillery, the amount of ammunition carried in units and extent to which stocks are held at unit or battery level.
The unit MBtu was defined as one thousand Btu, presumably from the Roman numeral system where " M " stands for one thousand ( 1, 000 ).
respectively, where e < sub > x </ sub >, e < sub > y </ sub >, e < sub > z </ sub > denotes the cartesian basis vectors ( all are orthogonal unit vectors ) and A < sub > x </ sub >, A < sub > y </ sub >, A < sub > z </ sub > are the corresponding coordinates, in the x, y, z directions.
More generally, an n-piece cubic Bézier curve can approximate a circle, when each inner control point is the distance from an outer control point on a unit circle, where t is 360 / n degrees, and n > 2.
where i is the imaginary unit.
Austria-Hungary asserted its right to extradite him, but Montenegrin authorities instead allowed the assassin to " escape " to Serbia where he joined Major Tankosić's unit ; Major Tankosić died in November 1915 covering the Serbian retreat, but not before confessing his role in the assassination to historians at Azania.
His manager, Margo Lewis, called 911 and airport security and Bo was immediately taken by ambulance to Creighton University Medical Center and admitted to the Intensive-care unit, where he stayed for several days.
where L, coastline length, a function of the measurement unit, ε, is approximated by the expression.
where are the direction cosines between the material and spatial coordinate systems with unit vectors and, respectively.
where i, j, and k are the unit vectors for the x -, y -, and z-axes, respectively.
Accordingly, when a disk was formatted or a disk error occurred, the unit would try to physically move the head 40 times in the direction of track zero ( although the 1541 DOS only used 35 tracks, the drive itself was a 40 track unit, so this ensured track zero would be reached no matter where the head was before ).
More scientific censuses were taken 1948 and 1959 where the enumeration unit was persons.
where u is a unit tangent vector.
Finally, weight of the chain is represented by ( 0, − λgs ) where λ is the mass per unit length, g is the acceleration of gravity and s is the length of chain between c and r.
If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation
Assuming that the strength of the cable is proportional to its density per unit length, the weight, w, per unit length of the chain can be written T / c, where c is constant, and the analysis for nonuniform chains can be applied.
where p is the natural length of the segment from c to r and λ < sub > 0 </ sub > is the mass per unit length of the spring with no tension and g is the acceleration of gravity.
where T is the magnitude of T and u is the unit tangent vector.
where is the force accelerating the object and the " hat " variables are unit direction vectors ( points in the centrifugal or outward direction, and is orthogonal to it ).
Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.
where is the unit vector in the direction of the z-axis.

where and vectors
where are the coordinate vectors in some frame of reference chosen for the problem ( See figure 1 ).
where is the coordinate radius, and are the test-particle's conserved energy and angular momentum respectively ( constructed from the killing vectors ).
where the are vectors of size n, then the determinant of A is defined so that
If y is a point where the vector field v ( y ) ≠ 0, then there is a change of coordinates for a region around y where the vector field becomes a series of parallel vectors of the same magnitude.
This is in contrast to an interval estimator, where the result would be a range of plausible values ( or vectors or functions ).
is the kinetic energy operator, where m is the mass of the particle, the dot denotes the dot product of vectors, and ;
In other words, physical states can be identified with equivalence classes of vectors of length 1 in H, where two vectors represent the same state if they differ only by a phase factor.
The components of a vector can respond in two distinct ways to a change of basis ( see covariance and contravariance of vectors ), where the new basis vectors are expressed in terms of the old basis vectors as,
where r is the distance from the axis of rotation to the particle, F is the magnitude of the force applied, and θ is the angle between the position and force vectors.
The relation between the tangent vectors defined earlier and derivations is as follows: if γ is a curve with tangent vector γ '( 0 ), then the corresponding derivation is D ( ƒ ) = ( ƒ ∘ γ )'( 0 ) ( where the derivative is taken in the ordinary sense, since ƒ ∘ γ is a function from (- 1, 1 ) to R ).
where v, v < sub > 1 </ sub > and v < sub > 2 </ sub > are vectors from V, while w, w < sub > 1 </ sub >, and w < sub > 2 </ sub > are vectors from W, and c is from the underlying field K. Denoting by R the space generated by these four equivalence relations, the tensor product of the two vector spaces V and W is then the quotient space
An important example is Minkowski space that is important to our understanding of special relativity, where there is a generalization of length that permits non-zero vectors to have zero length.
Other physical examples come from thermodynamics, where many of the quantities of interest can be considered vectors in a space with no notion of length or angle.
where a < sub > 1 </ sub >, a < sub > 2 </ sub >, a < sub > 3 </ sub > are called the vector components ( or vector projections ) of a on the basis vectors or, equivalently, on the corresponding Cartesian axes x, y, and z ( see figure ), while a < sub > 1 </ sub >, a < sub > 2 </ sub >, a < sub > 3 </ sub > are the respective scalar components ( or scalar projections ).

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