If you have a word with an abjective between parentheses where you would normally use an instead of a, should you do this in this case too?  It's a little hard for me to explain, so here a concrete example: (acoustic) piano.  Should it be a (acoustic) piano or an (acoustic) piano, since you can choose to not pronounce acoustic?
When a/an precedes a parenthetical aside (sometimes seen in informal/conversational writing), should the vowel rule depend on the first word in parentheses, or the next word in the "regular" flow of the sentence?     I need a (memorable) idiom (preceding an m word; use a)   or     I need an (memorable) idiom (preceding an i word; use an)
What's the origin of "I'm down with it"? I understand it's an expression of agreement. What exactly does it mean and where did it originate from? Eigen Values Proof a.) Let A and B be $n$ x $n$ matrices. Prove that the matrix products   $AB$  and $BA$ have the same eigenvalues.      b.) Prove that every eigenvalue of a matrix A is also an eigenvalue of   its transpose $A^T$. Also, prove that if v is an eigenvector of A with   eigenvalue $\lambda$ and w is an eigenvector of $A^T$ with a different   eigenvalue $\mu \ne \lambda$, then v and w are orthogonal vectors with   respect to the dot product.   For a, I know that if their eigenvalues are the same then their eigenvectors must relate too.    For the first part of b, is it similar to proving that the $det(A) =det (A^T)$? And, I do not know how to do the second part. Shortcuts in Objective-C to concatenate NSStrings Are there any shortcuts to (stringByAppendingString:) string concatenation in Objective-C, or shortcuts for working with NSString in general?  For example, I'd like to make:  NSString *myString = @"This"; NSString *test = [myString stringByAppendingString:@" is just a test"];   something more like:  string myString = "This"; string test = myString + " is just a test"; Are users' reputation scores on the home page supposed to stand out that much now? It seems a couple minutes ago, a change was applied to the styling of the homepage, with users' rep scores now being much darker (and standing out more):        Compare with the former light grey colouring (image courtesy of ):        Is this intentional? If so, why? It highlights something that's not really relevant, in my opinion. Trig sum: $\tan ^21^\circ+\tan ^22^\circ+\cdots+\tan^2 89^\circ = \text{?}$ As the title suggests, I'm trying to find the sum $$\tan^21^\circ+\tan^2 2^\circ+\cdots+\tan^2 89^\circ$$ I'm looking for a solution that doesn't involve complex numbers, or any other advanced branch in maths. The solution can involve techniques such as induction, telecoping, etc, but preferably only ideas from precalculus, e.g. trig identities, polynomials, etc.  EDIT: I know that the sum is a rational number. An  can be identified by its  together with isolating intervals with rational bounds for its real and imaginary parts. The degree of an algebraic number is the  of its minimal polynomial. There are known algorithms that allow to easily compute sum and product of algebraic numbers in this representation, raise them to a rational power, extract real and imaginary parts, compare them, or evaluate them numerically to an arbitrary precision.  Is there an efficient algorithm that given an algebraic number $\alpha$ in this representation can decide if $\alpha$ can be represented as a sum or product of algebraic numbers of smaller degree? gnome-desktop-item-edit: command not found on Ubuntu 19.10 and later even with the 'gnome-panel' package installed Why does Javascript getYear() return 108? Why does this javascript return 108 instead of 2008? it gets the day and month correct but not the year?  myDate = new Date(); year = myDate.getYear();   year = 108? Applications Don't Show Up in Spotlight Spotlight has stopped showing any results for my Applications. I've tried reindexing and removing the index so it rebuilds it. No change. I've tried adding Applications to the Privacy tab and removing it, no change.  I tried repairing disk permissions and redoing the above, no change. I've tried removing everything from the index except Applications and then I just get nothing for any search at all (except dictionary entries).  I tried adding a symlink in my homedir to Applications and reindexing, but no change.  Any ideas on what to do?  I'm running Snow Leopard.  This is driving me crazy!  Update: I've noticed that when I start a reindex with sudo mdutil -E / and then immediately do a Spotlight search for an app that the app shows up temporarily until Spotlight gets disabled due to active indexing.  After the indexing is done, the app entries go away. Is spacetime absolute? As I understand it Newton's Laws imply that space is relative, as the laws of physics are the same in all inertial frames and as such there is no way, even in principle, to distinguish a frame that is truly at rest (absolute space). Hence the concept is physically meaningless, and the positions of (and distances between) physical objects, events, etc. are relative to the frame in which one is observing them from. Advancing on to Special Relativity, by postulating that the speed of light (in vacuum) is constant in all frames of reference, we are forced to conclude that time is relative also (as if it weren't then different observers would observe a different speed of light (in vacuum)). This leads to the result that the concepts of space and time are no longer completely separate and independent of one another and instead intertwined (as an event that occurs at rest over some time period in one frame, will occur over some spatial interval and a different time interval in another frame). Hence they should be considered as should be considered as a single entity, called spacetime.  Sorry for the waffling so far, just want to check that my understanding is correct up to this point?!  My main question is, given that space and time are (individually) relative quantities, is spacetime itself relative, or can it be considered absolute (as after all, it is the mathematical space of all possible events and exists independently of the physical events that occur within it)? How to update to the latest numpy and scipy on Ubuntu 14.04LTS On my Ubuntu 14.04LTS, for python3, I have   &gt;&gt;&gt; import numpy  &gt;&gt;&gt; import scipy  &gt;&gt;&gt; numpy.__version__  '1.8.2'  &gt;&gt;&gt; scipy.__version__  '0.13.3'   I want to update numpy and scipy to the most , I tried with the following commands  sudo pip3 install --upgrade numpy sudo pip3 install --upgrade scipy   both commands ran successfully, but the version numbers didn't change to 1.9.2 and 0.16.0 at all for both python packages (after restarting the computer). Anyone knows how to update to the most version? Thank you very much!! Differences between ways to express future actions I asked this question  but I haven't gotten a useful answer. Could you tell me the difference in meaning between these sentences?        Do you think you will visit them next week?     Will you visit them next week?     Are you going to visit them next week?     Are you visiting them next week?     Are you going to be visiting them next week?     Are you planning to be visiting them next week?     Do you plan to visit them next week?      Will there be any difference in the answers?        I think I will visit them next week.     I will visit them next week.     I am going to visit them next week.     I am visiting them next week.     I am going to be visiting them next week.     I am planning to be visiting them next week.     I plan to visit them next week.      Can I use "planning to" instead of "going to"?  (E.g. "Are you planning to visit them next week? — Yes, I am planning to visit them next week.") Which of these sentences show that the subject of conversation has already been discussed? For example, I talked with a friend of mine about my plans to visit somebody. So my friend is aware of my plans.  And my last question. Which of these seven sentences express that the action will certainly take place? What prevents this magnetic perpetuum mobile from working? error in count script for number of occurences Dynamically access object property using variable Eclipse Shortcut to Split Long Strings I swear I've seen someone do this, but I can't find it in the various lists of shortcuts.  Given:  String s = "A very long ............................ String";   Is there an Eclipse shortcut to turn it into:  String s = "A very long ............................ "      + "String"; another balls and bins question I've seen many variations of this problem but I can't find a good, thorough explanation on how to solve it. I'm not just looking for a solution, but a step-by-step explanation on how to derive the solution.  So the problem at hand is:   You have m balls and n bins. Consider throwing each ball into a bin uniformly and at random.    What is the expected number of bins that are empty, in terms of m and n? What is the expected number of bins that contain exactly 1 ball, in terms of m and n?   How would I approach solving this problem?  Thanks! $\limsup$ and cluster points Let $(x_n)$ be a sequence in $\mathbb R$. We call $y$ a cluster point of $(x_n)$ iff for every neighborhood $N$ of $y$ there are infinitely many $n$ such that $x_n \in N$. Let $C$ denote the set of cluster points of $(x_n)$.   By definition, $\limsup_{n \to \infty} x_n = \inf_n \sup_{k \geq n} x_k$.  Can you show me how to prove $\limsup_n x_n = \sup C$? Thanks. Are repository updates secure?  As a bear of little brain from the developer side, I cannot understand why the repository list is http://security.ubuntu.com and the other http(unsecured) sites listed in /etc/apt/sources.list.  Without a certificate chain match this appears as "ask any responder for a list of packages to update" instead of "ask the ubuntu.com site..."  Can any network choose to spoof the update sites, and is this a common practice to provide a locally cached and vetted copy? What is the variance of the weighted mixture of two gaussians? Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and $q$ where $0\le p \le 1$ and $q = 1-p$. I know that the mean of this mixture would be $\mu_{AB} = (p\times\mu_A) + (q\times\mu_B)$.  What would the variance be?    A concrete example would be if I knew the parameters for the distribution of male and female height. If I had a room of people that was 60% male, I could produce the expected mean height for the whole room, but what about the variance?