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Thus, typical security concerns, such as AAA (pronounced tripleA, standing for administration, authorization, and authentication), which deal with how identity is established and managed, what kinds of access or capability proofs of identity confer, and how identity may be proven, are making themselves important in ongoing XML development and activity To that end, numerous XML markup languages incorporate or support various systems of digital signatures, extensions and management of con rmation and trust, and various proofs of identity and nonrepudiation of transactions (to.



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Two figures are congruent if one can be moved so that it exactly overlaps the other. A figure cut out of paper can be turned, slid, and flipped over to see if it matches up with another figure. If the figure is put on a graph, then these movements will change the coordinates of the points. A transformation is a way to describe such a change of coordinates.





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A transformation begins with a general description of a point, such as P(x, y) which represents a point P with coordinates x and y. Following this is an arrow A and then a description of the point s image, the place where it ends up after the move. Usually the image of P is called P, the image of A is called A , and so on. For example, the transformation P(x, y) A Pr(x 5, 4 y) means that the point A(2, 1) is moved to Ar(2 5, 4 1) Ar( 3, 3), the point B(3, 5) is moved to Br(3 5, 4 5) Br( 2, 1), and the point C(6, 1) is moved to Cr(6 5, 4 1) Cr(1, 3). This transformation flips the triangle ^ABC over and slides it to the left, as shown in Fig. 18-1.

Fig. 18-1

18.1 Using transformation notation Name the image of the points A(3, 1), B(3, 4), and C(5, 1) under the following transformations: (a) P(x, y) A Pr(x (b) Q(x, y) A Qr(x 2, y 5, y) 1)

12

(c) R(x, y) A Rr(5x, 5y)

(d) S(x, y) A Sr( y, x) (e) T(x, y) A Tr(y, 5

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(a) Ar(3 (b) A (3 2, 1 5, 1) 1) Ar(5, 0), Br(3 5, 4) 2, 4 1)

Br(5, 3), and Cr(5 5, 1)

2, 1 C (10, 1)

Cr(7, 0)

In This :

A (8, 1), Br(3

Br(8, 4), and C (5

(c) Ar(5 # 3, 5 # 1)

Ar(15, 5), Br(5 # 3, 5 # 4)

Br(15, 20), and Cr(5 # 5, 5 # 1)

prevent individuals from denying that they authorized such transactions later on). The document XML-Signature Syntax and Processing, a Recommendation approved on February 12, 2002, forms the basis for this chapter. It can be accessed at the W3C Web site at http://www.w3.org/TR/xmldsig-core/. The design philosophy for this Recommendation appears in XML-Signature Requirements, on the W3C Web site at http://www.w3.org/TR/ xmldsig-requirements. Just as a point of review, the W3C de ned Canonical XML as a Working Recommendation on March 15, 2001, stating the following:

Cr(25, 5)

(d) Ar( 1, 3), Br( 4, 3), and Cr( 1, 5) (e) Ar(1, 5 3) Ar(1, 2), Br(4, 5 3) Br(4, 2), and Cr(1, 5 5) Cr(1, 0)

Introduction Methods of Computing Interest Accounting for Notes Payable and Notes Receivable Discounting Dishonored Notes Receivable Recording Uncollectible Accounts Computing Uncollectible Accounts Recovery of Uncollectible Accounts Summary Solved Problems Introduction

A transformation that slides figures without flipping or rotating them is called a translation. The translation that slides everything to the right a units and up b units is P(x, y) A Pr(x a, y b).

Performing a translation Let rectangle ABCD be formed by A( 1, 4), B( 1, 3), C(3, 3), and D(3, 4). Graph rectangle ABCD and its image under the following translations: (a) P(x, y) A Pr(x (b) P(x, y) A Ps(x (c) P(x, y) A P-(x

Thus, in Fig. 2-27, j a > j b; this follows from Principle 4, since j a and j b are supplements of the same angle, j c.

Fig. 2-27

2.10 Applying basic theorems: principles 1 to 5 State the basic angle theorem needed to prove j a > j b in each part of Fig. 2-28.

Fig. 2-28

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