17. iPhone 手機，是使用___(18)___技術，讓使用者藉由螢幕直接來操控 iPhone 呢?

18. TB 等於___(19)___位元組(Bytes)？。

19. 處理器使用的所有指令稱為指令集，主要可以分為___(20)___和複雜指令集(Complex Instruction Set Computer, CISC)。

1. Define public history and discuss the work and roles of public historians.

2. A prominent historian recently declared that, "In a 'post-truth' age of 'alternative facts' and 'fake news,' historians must ask fundamental questions about our public roles. We might think of ourselves as above the fray; viewing developments with a certain detachment. But as soon as we enter the classroom, we become historical actors whose choices have broad consequences. We have a moral obligation to think seriously about how we, as a discipline, can help strengthen democratic institutions." Discuss this assertion and what it means for contemporary historians. 

3. "Only the vanquished remember history," or, "History is written by the victors." Discuss which claim is more true, and why? Give examples. 

4. Discuss recent trends to make the study of history more inclusive. Give examples. 

(a) Show that the input \(n\) signals are linearly independent.

(b) Please verify that if this mixer performs a linear transformation in this system.

(a) If the period of a set of periodic functions is \(2\pi\), what is the orthonormal basis of the vector space that these periodic functions belong to? You have to show the vectors in the basis are orthonormal to get full credit.

(b) From the spectral theorem, find a vector \(g(x)\) in a subspace spanned by only \(\{1, \cos(x), \cos(2x), \sin(x), \sin(2x)\}\) so that \(g(x)\) has the shortest distance to the function \(f(x) = x\) in the interval \([-\pi, \pi]\).Note: In this problem, you may need: \(\int x \sin ax dx = -\frac{x}{a} \cos ax + \frac{1}{a^2} \sin ax\) and \(\int x \cos ax dx = \frac{x}{a} \sin ax + \frac{1}{a^2} \cos ax\)

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