Can I fit a Minolta 35mm lens to a Micro 4third mount?
Can I use lens brand X on interchangeable lens camera brand Y?
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$ Suppose that $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging the first two rows of $A$. Prove that $\det(B) = -\det(A)$.  By general $n \times n$ matrix, I mean $$\left[\begin{matrix} a_{11} &amp; a_{12} &amp; \cdots &amp; a_{1n} \\ a_{21} &amp; a_{22} &amp; \cdots &amp; a_{2n} \\ \vdots &amp; \vdots &amp; \ddots &amp; \vdots \\ a_{n1} &amp; a_{n2} &amp; \cdots &amp; a_{nn} \end{matrix} \right]$$ I'm thinking of using the cofactor expansion of the 2nd row of the first matrix, yielding $$ \det(A) = c_{21} a_{21} + c_{22} a_{22} + \cdots+ c_{2n} a_{2n}  $$ which will be positive or negative depending on $n$ and the values of $a_{21}, \ldots,a_{2n}$, and using the same on the first row in matrix $B$ to get $c_{11} a_{21}$ etc. and then use the fact that the power of the $c$ subscripts will alter $\det(B)$ to be the opposite sign, but I'm not sure how to express all of this mathematically in a proof directly. Help please? Are $(\mathbb{R},+)$ and $(\mathbb{C},+)$ isomorphic as additive groups?  I know that there is a bijection between $\mathbb{R}$  and $\mathbb{C}$, and  asks whether they are isomorphic as abelian groups, are they referring to the additive abelian group? If so is there any simple isomorphism I can find? I know nothing about Hamel basis. Thanks. NSString instance reports its class as NSCFString My objective here is really simple -- I'm trying to set an NSString to some test data, then return the class, which should be NSString. Here's my code:  NSString* stringer = [NSString stringWithFormat: @"Test"]; NSLog(@"%@", [stringer class]);   The log says that the class is NSCFString, not NSString. What's going on here? Encopresis, I'm at my wits end? Does anybody have suggestions? My 12 year old daughter has been dealing with retentive encopresis since age 6. She avoids going to the toilet at all. This results in soiling and the production of an amazing huge toilet-clogging log-like object every week. We have been trying for years to get her to talk about this, but when we do talk about this, the response is ALWAYS "I don't know" despite what her pedi, GI doc and psychologist tried to do or suggested we do to get her to talk about it. We switched psychologists last year after a year of not talking about this, no luck.  We have tried so many treatment plans since diagnosis, specifically tailored to her, such as enemas, scheduled toilet sittings, rewards, consequences, psychologist, etc. she just keeps holding it in. Right before summer, her pedi and the GI doc laid out a clear treatment plan of laxatives, regular bathroom visits, and a rewards program. She did take the Miralax (2 table spoons) but she just kept holding it in and soiling her pants. She avoided going to the toilet. I made her stay at the toilet and told her "if you poop, I will buy you XYZ" (something she REALLY wants)" you can do XYZ only after you poop" and not letting her do things "you can't do XYZ until you poop" and XYZ would be something she LOVES to do. I wouldn't let her leave the toilet until she pooped, so she sat there for hours, no luck. When school started, she refuses to take the Miralax.  Now we laid out a new treatment plan. We TRIED to involve her, the response is again "I don't know." She is supposed to take an enema every morning and sit on the toilet, but she fights daily about taking it. When she does take it, she holds it in and won't sit on the toilet. There is also a diet plan she refuses to follow. She is not supposed to drink dairy, but drinks milk at school. Now the past 2 weeks she refused all treatment which we fight daily about. She refuses to sit on the toilet, no matter what we try. 2 years ago we tried ucanpooptoo, didn't help.  We asked her why she holds it in. Does pooping hurt? Does it scare you to poop? Does it feel good to hold it in? The answer is always "I don't know" and you can question her for hours and hear "I don't know". We explained to her digestion and she knows why she needs to poop. We ruled out any physiological reasons for retention. Luckily her friends don't notice, but one day her friends might smell her soiling, and I talked to her about this, how it would affect, boys , high school, etc. Her response was "I don't know" and she would not talk about this.  Does anybody have suggestions how to get her to start pooping in the toilet regularly? "How are" or "How is" the wife and kid? How are the wife and kid?   How is the wife and kid?      Which is more correct? Java generics T vs Object Why are Grothendieck's and Hartshorne's definitions of quasi-coherence equivalent? Hartshorne's Algebraic Geometry defines an $\mathcal O_X$-module $\mathscr F$ to be quasi-coherent if there is an open affine cover $(U_i=\operatorname{Spec} A_i)_{i\in\mathcal I}$ of $X$ such that each $\mathscr F\rvert_{U_i}$ is isomorphic to the sheaf of modules $\widetilde{M_i}$ associated to some $A_i$-module $M_i$. It is later proved that this is equivalent to the statement that for any open affine $U=\operatorname{Spec} A\subseteq X$, there exists an $A$-module $M$ with $\mathscr F\rvert_U\cong\widetilde M$.  On the other hand, Grothendieck's Éléments de Géométrie Algébrique defines $\mathscr F$ to be quasi-coherent if every point $x\in X$ admits an open neighborhood $U\subseteq X$ such that $\mathscr F\rvert_U$ is isomorphic to the cokernel of a morphism of free $\mathcal O_U$-modules.  Now I wonder how those definitions are equal. I tried proving it by myself, but both directions seem quite nontrivial to me... Any hints? What does % do to strings in Python? A linear operator commuting with all such operators is a scalar multiple of the identity. The question is from Axler's "Linear Algebra Done Right", which I'm using for self-study.  We are given a linear operator $T$ over a finite dimensional vector space $V$. We have to show that $T$ is a scalar multiple of the identity iff $\forall S \in {\cal L}(V), TS = ST$. Here, ${\cal L}(V)$ denotes the set of all linear operators over $V$.  One direction is easy to prove. If $T$ is a scalar multiple of the identity, then there exists a scalar $a$ such that $Tv = av$, $\forall v \in V$. Hence, given an arbitrary vector $w$, $$TS(w) = T(Sw) = a(Sw) = S(aw) = S(Tw) = ST(w)$$ where the third equality is possible because $S$ is a linear operator. Then, it follows that $TS = ST$, as required.  I am, however, at a loss as to how to tackle the other direction. I thought that a proof by contradiction,  ultimately constructing a linear operator $S$ for which $TS \neq ST$, might be the way to go, but haven't made much progress.   Thanks in advance! Difference between "per" and "a" What is Thanos's motivation for his action? If I had a gauntlet with essentially unlimited power, and my goal was to help make sure life in the universe was able to prosper, then my first thought toward this goal probably would not be      to extinguish half of all life.   This doesn't directly help anyone, and it is, at best, a temporary solution, since      populations will eventually grow back.   Assuming that I am not, in fact, secretly in love with an avatar of death itself, why would I choose to      commit universal genocide   instead of directly solving the limited resource problem?  So, to be specific, my question is: In-universe, what is Thanos's motivation for attempting to do this instead of more reasonable alternatives? Is it possible to disable X at boot time? I'm setting up a server so it would be nice if it wouldn't load the graphical interface every time I boot. "Recent Badges" list is displayed without margins on "Home" page When the &quot;Hide Hot Network Questions&quot; preference is enabled (i.e. HNQ sidebar is hidden), we see &quot;Recent Tags&quot; and &quot;Recent Badges&quot; in the homepage instead of the HNQ. However, the &quot;Recent Badges&quot; list is displayed with no margins. ex.)   I think that the appropriate margins were set in the past. cf.) Does tourist visa (90 days) apply after a long-term visa ends in Schengen countries? How do I temporarily disable an app when there is no "Disable" option Disable StringBuilder optimisation in javac Hiding sublayer with toggle button using LayerActions? I have a toggle map (like ) with sublayers. I want all the sublayers to be visible when you open the map, but I would like to hide some sublayers when the toggle buttons are clicked. I've tried adding a hide sublayer code into the LayerActions section of my code, but it's not hiding the sublayers (the button does the same function no matter whether the 'layer.getSubLayer(1).hide()' is there or not). This is the code I'm using:  var LayerActions = {  all: function(){   layer.getSubLayer(1).hide();   sublayers[0].setSQL("SELECT * FROM spreadsheet");   return true;  },  2011: function(){   layer.getSubLayer(1).hide();   sublayers[0].setSQL("SELECT * FROM spreadsheet WHERE year IN ('2011') AND year IS NOT NULL");   return true;  },  2012: function(){   layer.getSubLayer(1).hide();   sublayers[0].setSQL("SELECT * FROM spreadsheet WHERE year IN ('2012', '2012/2013') AND year IS NOT NULL");   return true;  } }   $('.button').click(function() {  $('.button').removeClass('selected');  $(this).addClass('selected');  LayerActions[$(this).attr('id')](); });   Could someone point me to where I'm messing up with my code? Or is it not possible to hide a sublayer using the LayerActions?    I'm now loading my layers differently, and this is my new code:   cartodb.createLayer(map, url1)     .addTo(map, 0)     .done(function (layer) {         console.log('added url1 ',url1);         cartodb.createLayer(map, url2)         .addTo(map, 1)         .done(function (layer) {             console.log('added url2 ',url2);         })         .error(function (){             console.log('problem adding 2nd layer');         });     })     .error(function () {         console.log('There is something wrong with requested data!');     });   So if I wanted to hide the first layer that's loaded (url1) and select only certain points from the second layer (url2), how would I code that in my LayerActions section? I've tried the following, but nothing changes when I click the buttons:  var LayerActions = { all: function(){   layer.getLayer(0).hide;   layer[1].setSQL("SELECT * FROM spreadsheet");   return true; }, 2011: function(){   layer.getLayer(0).hide;   layer[1].setSQL("SELECT * FROM spreadsheet WHERE year IN ('2011') AND year IS NOT NULL");   return true; }, ... Lets say an object is tied to a string and it is being swung in a circle:    In this case, the tension of the string acts as a centrifugal force that keeps the object moving in a circle. However, if centrifugal force is the only force acting on the object, why doesn't it collapse into the center? I am pretty sure this has to do with the object's inertia (or the centrifugal pseudo-force), where it moves slightly forward in a tangent before falling, restoring the orbit.  Also, what keeps the string taut during the swinging? There has to be some force countering the centripetal force that keeps the string tight. I think this might again have to do with the intertia/centrifugal pseudo-force but can a pseudo-force balance a real force? Also, if centripetal were to be balanced by the pseudo-force, wouldn't the object not move at all (since the net force would be 0)? Why can't two series-connected diodes act as a BJT? Another form of the question is: will joining two diodes with wires (pn-np) make a transistor-equivalent?  I read that they are not equivalent, but why? I am using this IC in boost converter configuration :   It steps up the voltage from 16.5V to 23V.   It drives a load current of 270mA.  I need to calculate the input current of the converter.   I understand that output power/input power is efficiency.   Since I know the output power, can I take the efficiency value from the graph 21 of the attached datasheet (86.8% approx - obtained from fig 21 graph) and find the input power?   With the input power, and since I know the input voltage, I can calculate the input current.   Is this the right way?   And I want to check if all the components at the output of the IC are properly rated.   Which parameters and components should I check and how to check?    Sorry for the poor image quality. The two transistors are taken from the SWE pin.