Pasting mm:ss into excel - gets mistakenly formatted as hh:mm
Entering Time data in excel in mm:ss format (without the leading 0: for the hours)
Given a sphere of radius $r$ with two spherical caps on it defined by the radii ($a_1$ and $a_2$) of the bases of the spherical caps, given a separation of the two spherical caps by angle $\theta$, how do you calculate the surface area of that intersection?   To clarify, the area is that of the curved surface on the sphere defined by the intersection. At the extreme where both $a_1,a_2 = r$, we would be describing a spherical lune.   Alternatively define the spherical caps by the angles  $\Phi_1 = \arcsin(a_1/r)$ and $\Phi_2 = \arcsin(a_2/r)$. Why does Skynet take prisoners? In the Terminator franchise, extermination camps are often mentioned. But from a machine-logic POV, wouldn't it make more sense to just kill all humans on sight, period? Or herd them into small areas and nuke them? (even today's military electronics are hardened against EMPs and Skynet wouldn't care about the environment.)   IIRC, the reasoning behind ghettoization / concentration camps / extermination camps / gas "showers" is to misdirect or mislead people both inside and outside the country as to what was really going on. But Skynet doesn't have to worry about bad publicity, and can manufacture all the free labor it needs. Is there any in-universe explanation for keeping large groups prisoners? Is there an efficient way to copy text from a PDF without the line breaks? Can you cast Mirror Image twice on successive turns and have 6 duplicates of yourself instead of 3? (PHB, pg. 260) is a spell that has a casting time of 1 action, and a duration of 1 minute. My question is, can you cast Mirror image twice on successive turns, gaining 6 images by turn 2?  Sample Turns:  Turn 1: Mirror Image (3 images)  Turn 2: Mirror Image again (6 images, with 3 of them lasting 1 turn less)  Since Mirror Image doesn't require concentration, there should be no interference between the 2 casts in terms of concentration. I know that this could be up to DM Fiat, but I was wondering if there was a proper interpretation of the printed rules for this situation. Number of solutions to the congruence $x^q \equiv 1 \mod p$. Let $p, q$ be distinct odd primes, I would like to compute the number of solution $\mod p$ to the congruence $x^q \equiv 1 \mod p$. (Show that it's $gcd(q, p - 1))$  If $x^q \equiv 1 \mod p$, since $q$ is prime, this must mean that $x$ is either $1$ or has order $q$.   Hence, the problem reduces to finding the number of elements of $U_p$ which is either $1$ or has order $q$.  If $ q \nmid  p - 1$, then there is only one element, namely $1$.  If $q \mid p - 1$, then the number of elements of order $q$ is $\phi(q) = q - 1$, and so the number of solutions to the congruence $\mod p$ is $q - 1 + 1 = q$, and in either case the number of solutions is $\gcd(q, p - 1)$.  Does this look fine? A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix many Servers of SQL server 2012 needs mirroring An explanation of Hawking Radiation How to make the taskbar blink my application like Messenger does when a new message arrive? vertical lines in matrix using tikz package my problem is interconnected to my two previous posts ( and) and i've tried to incorporate answers into solution but without success.   My task is this matrix multiplication with added description:   and my so far code follows:  \documentclass{article} \usepackage{tikz,amsmath}  \begin{document} \begin{tikzpicture} \node[minimum height=0cm,minimum width=2cm] (m) {}; \path[shade,draw] (0,2) -- (0,5) -- (3,5) -- (3,0); \draw (0,0) --(0,5); \draw (3,0) --(0,2); \draw (3,0) --(3,5); \node (r11) at ([xshift=0.6cm,yshift=4cm]m.south) {$S_{11}$}; \node (r11) at ([xshift=2.5cm,yshift=4cm]m.south) {$S_{12}$}; \node (r11) at ([xshift=2.5cm,yshift=2.15cm]m.south) {$S_{22}$}; \node (r11) at ([xshift=0.6cm,yshift=2.15cm]m.south) {$S_{21}$}; \node (r11) at ([xshift=0.6cm,yshift=2.6cm]m.south) {$--------------$}; \node (r11) at ([xshift=0.6cm,yshift=1.5cm]m.south) {$--------------$}; \end{tikzpicture} \[ \begin{bmatrix} \begin{equation}        wn_{1}           \\[0.3em]        wn_{2}       \end{bmatrix}  \]  \end{document}       with following output:      I am not able to add vertical line and nodes and incorporate the matrix into document (vector that follows behind the matrix is not centered). Problem with nodes and incorporation is the same as in . Is your mount an enemy of your target in terms of triggering sneak attack? I was working on building a Zorro character and this question came up: if a rogue is riding on a mount, is that mount considered an ally, or, specifically, an "enemy" of your target?  One of the ways Sneak attack can be trigged is...     "... if another enemy of the target is within 5 feet of it, that enemy   isn’t incapacitated, and you don’t have disadvantage on the attack   roll."   My assumption is yes. Every mount I'm aware of has some kind of attack at its disposal, and thus they represent a threat to your target in addition to the increased threat potential they grant you as the rider. Moreover, if a gnome can proc a sneak attack by acting as a distraction, I don't know why a warhorse wouldn't be able to. That said, is there anything in the books or elsewhere that defines what "enemy of the target" is allowed to include? Axis with trigonometric labels in PGFPlots How do I make the axis labels use multiples of \pi in PGFPlots? Is there a way to give a profile a different default list view then "Recently Viewed" in Lightning? The default font is too small on my screen at the resolution I have it, so I like to reset the font to size 12, but it appears I have to do this everytime I launch the program.  How do I make it remember my preferences? sObject ' ' type is not supported Hey everyone I've been seeing this a lot lately and am trying to figure out why this error is thrown when querying the SOAP API directly. I've tried several very basic SOQL queries such as  SELECT Body FROM AssetFeed   Only to be met with the sObject type 'AssetFeed' is not supported. error.  The account that I'm currently querying is just a standard user who accepted permission from an app that was created by a Developer Account, so I'm wondering if it might be permissions from the user or permission from the app itself? Possibly because Developer accounts cannot use 95% of whats offered?  The WSDL used is a v27.0 generated Partner WSDL if that helps narrow it down.  I've noticed this in multiple standard objects, so I'm wondering what the trend really is? Seems like a good informational question for future googling of others?  Running describeGlobal()  Array (     [0] =&gt; AggregateResult     [1] =&gt; Attachment     [2] =&gt; ChatterActivity     [3] =&gt; CollaborationGroup     [4] =&gt; CollaborationGroupFeed     [5] =&gt; CollaborationGroupMember     [6] =&gt; CollaborationGroupMemberRequest     [7] =&gt; CollaborationInvitation     [8] =&gt; ContentDocument     [9] =&gt; ContentDocumentFeed     [10] =&gt; ContentDocumentHistory     [11] =&gt; ContentDocumentLink     [12] =&gt; ContentVersion     [13] =&gt; ContentVersionHistory     [14] =&gt; EntitySubscription     [15] =&gt; FeedComment     [16] =&gt; FeedItem     [17] =&gt; FeedLike     [18] =&gt; FeedTrackedChange     [19] =&gt; Group     [20] =&gt; GroupMember     [21] =&gt; HashtagDefinition     [22] =&gt; Name     [23] =&gt; TaskPriority     [24] =&gt; TaskStatus     [25] =&gt; User     [26] =&gt; UserFeed     [27] =&gt; UserPreference     [28] =&gt; UserRecordAccess     [29] =&gt; UserRole )   Where would all the rest of my SOAP SObjects be? This seems like a very thin list compared to the 295 SObjects advertised How to prove whether a matrix has rank $1$ If $u$ $∈ \mathbb R^{m \times 1}$ and $v ∈ \mathbb R^{n \times 1}$ how do you show that the $(m \times  n)$ matrix $uv^T$ has rank $1$? Would providing an example be sufficient to prove it? Moment of inertia of a hollow sphere wrt the centre? I've been trying to compute the moment of inertia of a uniform hollow sphere (thin walled) wrt the centre, but I'm not quite sure what was wrong with my initial attempt (I've come to the correct answer now with a different method). Ok, here was my first method:  Consider a uniform hollow sphere of radius $R$ and mass $M$. On the hollow sphere, consider a concentric ring of radius $r$ and thickness $\text{d}x$. The mass of the ring is therefore $\text{d}m = \frac{M}{4\pi R^2}\cdot 2\pi r\cdot\text{d}x$. Now, use $r^2 = R^2 - x^2:$ $$\text{d}m = \frac{M}{4\pi R^2}\cdot 2\pi \left(R^2 - x^2 \right)^{1/2}\text{d}x$$ and the moment of inertia of a ring wrt the centre is $I = MR^2$, therefore: $$\text{d}I = \text{d}m\cdot r^2 = \frac{M}{4\pi R^2}\cdot 2\pi\left(R^2 - x^2\right)^{3/2}\text{d}x $$ Integrating to get the total moment of inertia: $$I = \int_{-R}^{R} \frac{M}{4\pi R^2} \cdot 2\pi\cdot \left(R^2 - x^2\right)^{3/2}\ \text{d}x = \frac{3MR^2 \pi}{16}$$  which obviously isn't correct as the real moment of inertia wrt the centre is $\frac{2MR^2}{3}$.   What was wrong with this method? Was it how I constructed the element? Any help would be appreciated, thanks very much. For about 2 days I'm trying to configure Ubuntu so that I can send an email, but when I type in:  echo "Subject: sendmail test" | sendmail -v my@email.com   I'll get:  postdrop: warning: unable to look up public/pickup: No such file or directory Mail Delivery Status Report will be mailed to &lt;andreigbr&gt;.   Even if I change my@email with mine, the inbox will be empty. Can somebody help me, please? I watched about 5 tutorial about how to send an email fom the command line but still doesn't work. What does the operator "<<" mean in C#? Atmospheric pressure experiment using a cup with a fluid to hold a glass plate When I was in high school, my teacher did an experiment to show the power of atmospheric pressure.  Experiment: Prepare a glass bottle, fill with water, put a glass plate on the bottle, make sure there is no air in the bottle, just water. Hold the glass bottle and plate, and invert them. Slowly, release the hand which hold the plate. Because the atmospheric pressure, the glass plate will not fall down.    Question 1: As we know, if we didn't put water into the glass bottle, just air in the glass bottle the glass plate will fall down. So, If we use other liquid instead of water, this liquid has smaller density than water, like alcohol, the plate will not fall down. But, if we continue to chose the smaller density liquid until the liquid has density like air the plate will fall down. So, if there is a threshold density of liquid make the plate between falling  down and not falling down?  Question 2: If we put the bottle and plate into water slowly, when the plate and part of bottle are in the water but part of the bottle still above the water, will the plate fall down?  Question 3: Continuing question 2, when both bottle and plate are in the water I know the plate will fall down. So, how does the pressure of water and atmosphere change?  Is there a good description of this phenomena?  Why does the trick continue to work with lower density fluids and why does placing the plate in the water cause it to fall?