Consider two column vectors such that $a = (1,2,3)^T$ and $b = (-3,3,-1)^T$.   What is the geometric relationship between $a$ and $b$?
which vectors are perpendicular to each other?  $\vec a = (1, -2, 3)$, $\vec b = (5, 4, 1)$, $\vec c = (1, 0, -5)$  Do i just take the dot product of 2 of them. If the dot product they are at $90^\circ$? But how do i know if there perpendicular?
Short example of regular expression converted to a state machine? I see this often in the build scripts of projects that use autotools (autoconf, automake).  When somebody wants to check the value of a shell variable, they frequently use this idiom:  if test "x$SHELL_VAR" = "xyes"; then ...   What is the advantage to this over simply checking the value like this:  if test $SHELL_VAR = "yes"; then ...   I figure there must be some reason that I see this so often, but I can't figure out what it is. Turning a cipher into a hashing function Riemann integrabilty of an indicator function Consider the following function on $[0,1]$:   $$f(x)=\begin{cases}1&amp;x\in\{a_1,a_2,\dots,a_n\}\\0 &amp;\text{otherwise}\end{cases}$$   The $a_i$ are fixed and all in $[0,1]$. Determine whether $f$ is Riemintegrable or not.   By the Riemann&ndash;Lebesgue criterion $f$ is Riemann integrable. How to prove directly? Merging two SQLite databases which both have junction tables I noticed that, for each research project, there comes a point where I have to consult the literature, and find all the previous research related to the current project.  Unfortunately, I seem to be very inefficient in my approach. I spend a lot of time digging through papers that are really interesting, but only of tangential importance to my current work, just to find the few papers that actually do similar things. (The pile of "cool paper, read when time" just keeps growing.)  Hence, I'm wondering: What is the most time efficient way to get a thorough overview of the literature in a specific niche of a field?    While searching for an answer I came across these questions:   - This question is quite similar and I liked the approach. I debated with myself if this is a duplicate, but I think it is focused more on how to be sure the search was exhaustive, whereas I'm worried about time efficiency. (Also, I'm a bit curious if things have changed since 2012.)   - The answer provides tips on how to identify what literature generally is important in a field, but I am looking for the most cost effective (least time consuming) way to do it in an area, where I know the broad literature, but not the specifics. How does the Golden Ratio/Spiral Work? Is it useful with Logo Design? using this command I changed root password   mysqladmin -u root password fg$pkh@567fghu   And now I cant access mysql. Is this because mysql parse the chars other than what I expect?  Also I completely removed and installed mysql and Problem is extant. How do I remove mysql so that I get rid of password? Problems with fonts I'm an average user of LaTeX, but not proficiency. I'm trying to learn from book templates I've found on the web, but I get this error message:  Trying to make PK font ccicons at 1493 DPI... Running miktex-makemf.exe... miktex-makemf: The ccicons source file could not be found. Running ttf2pk.exe... miktex-makemf: PK font ccicons could not be created.  LaTeX Font Warning: Some font shapes were not available, defaults substituted.  !pdfTeX error: pdflatex.exe (file ccicons): Font ccicons at 1493 not found  ==&gt; Fatal error occurred, no output PDF file produced!   I'm using MiKTeX (over Windows 7), and according to the MiKTeX package manager the "ccicons" package is already installed.  Could you please help me solve this problem? Using Sequence to delete a part of an expression For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$? $$x^n-a$$  So $n$ is any integer greater than 1, and $a$ is any integer.  $a$ being any integer is where I am running into trouble.  I have already shown and worked out a proof for this being irreducible when a is prime.  Now I am just working through examples, trying to figure out a pattern.  The exercise is asking for application of Eisenstein's Criterion only, so I am assuming that the value of n should have no effect on the irreducibility. In my work, we are comparing predicted rankings versus true rankings for some sets of data. Up until recently, we've been using Kendall-Tau alone. A group working on a similar project suggested we try to use the  instead, and that they preferred it. I was wondering what the differences between the different rank correlation algorithms were.  The best I've found was , which claims Spearman is used in place of usual linear correlations, and that Kendall-Tau is less direct and more closely resembles Goodman-Kruskal Gamma. The data I'm working with doesn't seem to have any obvious linear correlations, and the data is heavily skewed and non-normal.  Also, Spearman generally reports higher correlation than Kendall-Tau for our data, and I was wondering what that says about the data specifically. I'm not a statistician, so some of the papers I'm reading on these things just seem like jargon to me, sorry. Why isn't an upgrade to 20.04 from 18.04 available yet? Upon system restart, dconf editor doesn't save changes I can use the dconf-editor to change my touchpad settings to natural scrolling, but upon system restart the settings get reverted. (But not on sleep or hibernate.) When I open the editor, the option is still orange indicating it has been changed. when I uncheck and recheck the natural scroll option, it is re-enabled. Is there a fix, or am I changing the wrong option? The path is org > gnome > settings-daemon > peripherals > touchpad > natural-scroll.  Currently running 13.10 Using 'very' with a noun Using oscilloscope safely with AC mains I know there is quite few discussions already on this topic, but since English isn't my first language, I though it better to get some more information about this.  I have used oscilloscopes to troubleshoot electronics problems and measure AC engine current spikes at startup, but I have no experience using them to measure high voltage levels and my experience is with old analog scopes.  So now I have this new DSO and the input rating is 400V peak to peak AC, so it can handle about 140V AC RMS? Not that I'm going to input that much there.  Since I live in Europe the mains here are 230 V @ 50 Hz I can't measure them directly.  If I set the attenuation from the scope and probe to 10X, the voltage is 23 RMS and it is safe to measure? And yes the probes are rated for 1kV.  If that is true, it's also safe to measure voltage between two main lines (400V RMS), since the peak-to-peak would be about 112 volts?  SAFETY: When I am measuring AC, I will be using the scope from its internal battery or with a isolating transformer (1:1) so that it is floating, meaning that there is no connection to earth ground. Are there any other safety issues I have not realized? I want to select questions that are only tagged as SQL, SQLServer, SQLSever 2008. I am not interested in questions that have anything more than these tags. How do i select such questions only ? Is there a Windows 10 Hotkey or Shortcut for switching to a specific display? I have my Windows 10 desktop computer connected to two displays through HDMI - one monitor and one TV, which I can toggle through with Windows Key+P as described in the accepted answer to .  However, I was wondering if there was some hotkey, shortcut, or button combination I could use sort of like a "Virtual KVM Switch" that lets me select one display or another specifically, without needing to cycle/toggle through other displays. What are all the correct answers to the Squirrel's questions, and what is the reward when I get them all correct? How to record how much time user has spent on my node? I want to record the time a user has spent on my particular node so I could show a pop up to the user to register once the user has read 3 article. But the user must have spent at least 30 seconds on each node.   There is the  module available, but I wonder if I can merge it with another (custom) module I have created (which records the number of nodes user have visited)?