INSTRUCTOR WITH STUDENT ABOARD ON XCOUNTRY FLT HAS NMAC WITH B737.

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THIS WAS STUDENT'S FIRST XCOUNTRY FLT. WE DEPARTED NUT TREE; OUR START POINT WAS TRAVIS ARPT TO MYV AND RETURN TO NUT TREE. OUR CRUISE ALT WAS 5500 FT MSL; OUR MAGNETIC COURSE WAS 004 DEGS AND MAGNETIC HDG 357 DEGS. WE CALLED SAC APCH OVER DAVIS FOR ADVISORY TO MYV. ATC GAVE US A SQUAWK BUT DID NOT IDENT US FOR RADAR CONTACT FOR SEVERAL MINS. MY TRAINEE WAS TRYING TO MAKE CONTACT WITH ATC TO GET RADAR IDENTED BUT HE WAS HAVING TROUBLE GETTING ON TO THE FREQ. ATC WAS VERY BUSY. I DON'T REMEMBER THIS BUT MY TRAINEE SAID ATC HANDED US OVER TO NEXT CTLR. THEN AFTER THE HDOF IS WHEN INCIDENT OCCURRED. I DON'T REMEMBER IF WE WERE HANDED OFF OR NOT. WHILE WAITING TO BE RADAR IDENTED I TURNED AND LOOKED OVER MY R SHOULDER AND SAW ACR B737 AT 4 O'CLOCK POS; SAME ALT. B737 WAS TURNING R; I TURNED HARD L AND WE AVOIDED COLLISION. AFTER THAT MAYBE 2 OR 3 MINS WE TRIED TO GET HOLD OF ATC AND THEY SAID WE WERE NOT RADAR IDENTED; BUT DURING THAT EXCHANGE HE SAID RADAR CONTACT. AFTER THAT THE FLT WENT WELL. THE NEXT DAY AFTER TALKING TO THE TRAINEE HE INFORMED ME OUR XPONDER WAS IN STANDBY MODE. IF XPONDER WOULD HAVE BEEN ON THIS WHOLE INCIDENT WOULD HAVE BEEN AVOIDED. ALSO; IF ATC HAD NOT BEEN SO BUSY WE OR THEY MIGHT HAVE REALIZED WE WERE NOT IDENTED SOONER AND ASKED US TO CHK XPONDER ON.